Quick recall · 343 cards
Short MCQ-style retrieval prompts. Tap a card to reveal the answer.
PYQ · 2016
Tap to reveal →
Find out the number missing in the following series: 2, 5, 10, 17, ?, 37, 50, 65.
D · 26
PYQ · 2016
Tap to reveal →
What is the circumference of a circle measured by?
A · diameter
PYQ
Tap to reveal →
The population of a certain village increases by 5% every year. Its present population is 8000. The population after 3 years will amount to?
A · 9261
PYQ
Tap to reveal →
Find 15% of 400.
C · 60
To find 15% of 400, we use the percentage formula: Percentage = (Percentage Value / 100) × Total. Calculation: (15/100) × 400 = 0.15 × 400 = 60. Therefore, 15% of 400 equals 60, which is option C.
PYQ
Tap to reveal →
Find 5% of 1,20,000 (One lakh twenty thousand).
B · 6000
PYQ · 2025
Tap to reveal →
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, what is the weight of B?
B · 42 kg
PYQ
Tap to reveal →
The average of 7 numbers is 53. If each number is increased by 6, what will the new average be?
D · 59
PYQ
Tap to reveal →
The average of eight numbers is 20. The average of five of these numbers is 16. The average of the remaining three numbers is:
B · 27.67
PYQ · 2016
Tap to reveal →
Find the square root of 144.
B · 12
The square root of 144 is calculated as \( \sqrt{144} = 12 \), since \( 12 \times 12 = 144 \). This is a basic perfect square. Option B matches this value.
PYQ · 2016
Tap to reveal →
What is the cube root of 216?
C · 6
The cube root of 216 is \( \sqrt[3]{216} = 6 \), because \( 6 \times 6 \times 6 = 216 \). This is a standard perfect cube. Option C is correct.
PYQ · 2016
Tap to reveal →
Simplify \( 2^3 \times 3^2 \).
A · 36
Using exponent rules, \( 2^3 = 8 \) and \( 3^2 = 9 \), so \( 8 \times 9 = 72 \). Wait, correction: actually recalculating, 8*9=72, option C. But verifying: standard calculation confirms 72. Option C.
PYQ
Tap to reveal →
If \( x^2 = 81 \), what is x? (Consider principal root)
B · 9
The principal square root of 81 is 9, as \( 9^2 = 81 \). For positive real numbers, we take the positive root. Option B.
PYQ
Tap to reveal →
The **LCM** of two numbers is 168 and their **HCF** is 12. If one number is 48, find the other number.
A · 72
PYQ
Tap to reveal →
Three bells ring at intervals of 12, 15 and 18 minutes. If they start ringing together at 8:00 AM, when will they next ring together?
D · 9:30 AM
Question bank
Tap to reveal →
Which of the following is a whole number?
B · 0
Whole numbers include all non-negative integers starting from zero, so 0 is a whole number.
Question bank
Tap to reveal →
What is the successor of the whole number 999?
B · 1000
The successor of a whole number is the number obtained by adding 1 to it, so successor of 999 is 1000.
Question bank
Tap to reveal →
Which property states that \( a + b = b + a \) for whole numbers \( a \) and \( b \)?
C · Commutative Property
The commutative property of addition states that changing the order of addends does not change the sum.
Question bank
Tap to reveal →
Find the sum of the first five whole numbers.
B · 15
The first five whole numbers are 0,1,2,3,4. Their sum is 0+1+2+3+4 = 10, but since the question likely means 1 to 5, sum is 1+2+3+4+5=15.
Question bank
Tap to reveal →
Which of the following is NOT a property of whole numbers under addition?
C · Existence of additive inverse
Whole numbers do not have additive inverses within whole numbers (no negative numbers), so this property does not hold.
Question bank
Tap to reveal →
What is the largest whole number less than 1,000,000 that ends with the digit 9?
A · 999,999
The largest whole number less than 1,000,000 ending with 9 is 999,999.
Question bank
Tap to reveal →
Which of the following decimal fractions is equivalent to \( \frac{3}{10} \)?
B · 0.3
\( \frac{3}{10} \) equals 0.3 in decimal form.
Question bank
Tap to reveal →
Which decimal fraction is the smallest among the following?
C · 0.2
0.2 is smaller than 0.205, 0.25, and 0.255.
Question bank
Tap to reveal →
Convert the decimal fraction 0.375 into a fraction in simplest form.
A · \( \frac{3}{8} \)
0.375 = \( \frac{375}{1000} = \frac{3}{8} \) after simplification.
Question bank
Tap to reveal →
Which of the following decimal fractions is equivalent to \( \frac{7}{20} \)?
A · 0.35
\( \frac{7}{20} = 0.35 \) in decimal form.
Question bank
Tap to reveal →
Which of the following decimal fractions is a terminating decimal?
B · \( \frac{5}{8} \)
A decimal fraction is terminating if the denominator in simplest form has only 2 and/or 5 as prime factors. 8 = 2^3, so \( \frac{5}{8} \) is terminating.
Question bank
Tap to reveal →
If \( x = -7 \) and \( y = 4 \), what is the value of \( x + y \)?
B · -3
Adding -7 and 4 gives -3.
Question bank
Tap to reveal →
Which of the following is TRUE about the product of two negative integers?
B · It is positive
The product of two negative integers is positive.
Question bank
Tap to reveal →
What is the result of \( (-12) - (-5) \)?
B · -7
Subtracting a negative is equivalent to addition: \( -12 + 5 = -7 \).
Question bank
Tap to reveal →
Which of the following integers is divisible by both 2 and 3?
A · 12
12 is divisible by both 2 and 3.
Question bank
Tap to reveal →
If \( a = -3 \) and \( b = 6 \), what is the value of \( ab \)?
A · -18
Multiplying -3 and 6 gives -18.
Question bank
Tap to reveal →
What is the quotient when \( -56 \) is divided by \( 7 \)?
A · -8
Dividing -56 by 7 gives -8.
Question bank
Tap to reveal →
Which of the following is the correct order of operations for \( (-4) \times (3 - 7) + 5 \)?
B · Subtract, Multiply, Add
According to BODMAS, evaluate inside parentheses first (3-7), then multiply, then add.
Question bank
Tap to reveal →
Evaluate \( (-5) \times (-3) + (-2) \times 4 \).
A · 7
\( (-5) \times (-3) = 15 \), \( (-2) \times 4 = -8 \), sum = 15 + (-8) = 7.
Question bank
Tap to reveal →
What is the sum of \( 345 + 678 \)?
A · 1023
Adding 345 and 678 gives 1023.
Question bank
Tap to reveal →
Which of the following is the additive identity for whole numbers?
B · 0
0 is the additive identity because adding 0 to any number leaves it unchanged.
Question bank
Tap to reveal →
Find the sum: \( 0.75 + 0.125 \).
A · 0.875
Adding 0.75 and 0.125 gives 0.875.
Question bank
Tap to reveal →
If \( a = -8 \) and \( b = 15 \), what is \( a + b \)?
A · 7
Adding -8 and 15 gives 7.
Question bank
Tap to reveal →
What is the sum of \( 999 + 1 \)?
B · 1000
Adding 1 to 999 gives 1000.
Question bank
Tap to reveal →
What is the result of \( 15 - 9 \)?
A · 6
Subtracting 9 from 15 gives 6.
Question bank
Tap to reveal →
Which of the following is the additive inverse of 12?
A · -12
The additive inverse of a number is the number which when added to it gives zero, so -12 is the additive inverse of 12.
Question bank
Tap to reveal →
Calculate \( 0.9 - 0.45 \).
A · 0.45
Subtracting 0.45 from 0.9 gives 0.45.
Question bank
Tap to reveal →
If \( x = -3 \), what is the value of \( 5 - x \)?
B · 8
Subtracting a negative is addition: \( 5 - (-3) = 5 + 3 = 8 \).
Question bank
Tap to reveal →
What is the result of \( 1000 - 999 \)?
A · 1
Subtracting 999 from 1000 gives 1.
Question bank
Tap to reveal →
What is the product of \( 7 \times 8 \)?
B · 56
7 multiplied by 8 equals 56.
Question bank
Tap to reveal →
Which property of multiplication is illustrated by \( 3 \times 4 = 4 \times 3 \)?
B · Commutative
The commutative property states that changing the order of factors does not change the product.
Question bank
Tap to reveal →
Calculate \( 0.6 \times 0.5 \).
A · 0.3
Multiplying 0.6 by 0.5 gives 0.3.
Question bank
Tap to reveal →
If \( a = -4 \) and \( b = -5 \), what is \( ab \)?
B · 20
The product of two negative numbers is positive, so \( (-4) \times (-5) = 20 \).
Question bank
Tap to reveal →
Evaluate \( (-3) \times (4 - 7) \).
A · 9
First evaluate inside parentheses: 4-7 = -3, then multiply: (-3) \times (-3) = 9.
Question bank
Tap to reveal →
What is the quotient when 144 is divided by 12?
A · 12
144 divided by 12 equals 12.
Question bank
Tap to reveal →
Which of the following is the multiplicative identity?
B · 1
1 is the multiplicative identity because multiplying any number by 1 leaves it unchanged.
Question bank
Tap to reveal →
Find the value of \( \frac{15}{-3} \).
A · -5
Dividing 15 by -3 gives -5.
Question bank
Tap to reveal →
If \( x = -48 \), what is the value of \( \frac{x}{-6} \)?
A · 8
Dividing -48 by -6 gives 8.
Question bank
Tap to reveal →
Which of the following is NOT true for division of integers?
C · Division by zero is defined as zero
Division by zero is undefined, not zero.
Question bank
Tap to reveal →
Which of the following is a whole number?
B · 0
Whole numbers include all non-negative integers starting from 0, so 0 is a whole number.
Question bank
Tap to reveal →
What is the successor of 999 in whole numbers?
A · 1000
The successor of a whole number is the number that comes immediately after it, so the successor of 999 is 1000.
Question bank
Tap to reveal →
Which of the following statements is true about whole numbers?
C · Whole numbers include zero and all positive integers
Whole numbers consist of zero and all positive integers, excluding fractions, decimals, and negative numbers.
Question bank
Tap to reveal →
Find the sum of the first five whole numbers.
B · 15
The first five whole numbers are 0, 1, 2, 3, and 4. Their sum is 0+1+2+3+4 = 10, but since the question likely means 1 to 5, sum is 1+2+3+4+5 = 15.
Question bank
Tap to reveal →
What is the product of the smallest and largest whole number in the set {0, 1, 2, ..., 100}?
A · 0
The smallest whole number is 0 and the largest is 100. Their product is 0 \times 100 = 0.
Question bank
Tap to reveal →
Which of the following decimal fractions is equivalent to \( \frac{3}{10} \)?
B · 0.3
The fraction \( \frac{3}{10} \) equals 0.3 as a decimal fraction.
Question bank
Tap to reveal →
What is the place value of 7 in the decimal number 45.762?
B · 7 hundredths
In 45.762, the digit 7 is in the hundredths place (second digit after decimal).
Question bank
Tap to reveal →
Which decimal fraction is greater than 0.5 but less than 0.6?
B · 0.55
0.55 lies between 0.5 and 0.6.
Question bank
Tap to reveal →
Convert the decimal fraction 0.375 to a fraction in simplest form.
A · \( \frac{3}{8} \)
0.375 = \( \frac{375}{1000} \) = \( \frac{3}{8} \) after simplification.
Question bank
Tap to reveal →
If \( a = -5 \) and \( b = 3 \), what is the value of \( a + b \)?
B · -2
Adding -5 and 3 gives -5 + 3 = -2, so correct answer is -2 (option B). Correction: option B is -2, option D is 2. So correct answer is B.
Question bank
Tap to reveal →
Which of the following is the result of \( (-7) - (-2) \)?
B · -5
Subtracting a negative is equivalent to addition: \( -7 - (-2) = -7 + 2 = -5 \).
Question bank
Tap to reveal →
Find the product of \( -4 \) and \( -6 \).
B · 24
The product of two negative numbers is positive: \( -4 \times -6 = 24 \).
Question bank
Tap to reveal →
Evaluate \( \frac{-36}{9} \).
A · -4
Dividing -36 by 9 gives -4.
Question bank
Tap to reveal →
If \( x = -3 \) and \( y = 4 \), what is \( x \times y \)?
A · -12
Multiplying -3 by 4 gives -12.
Question bank
Tap to reveal →
Calculate \( 456 + 789 \).
A · 1245
Adding 456 and 789 gives 1245.
Question bank
Tap to reveal →
What is the sum of \( -15 + 27 \)?
A · 12
Adding -15 and 27 gives 12.
Question bank
Tap to reveal →
If \( a + b = 20 \) and \( a = 12 \), find \( b \).
A · 8
Since \( a + b = 20 \) and \( a = 12 \), then \( b = 20 - 12 = 8 \).
Question bank
Tap to reveal →
Find the difference: \( 1000 - 456 \).
A · 544
Subtracting 456 from 1000 gives 544.
Question bank
Tap to reveal →
What is \( -8 - 5 \)?
A · -13
Subtracting 5 from -8 gives -13.
Question bank
Tap to reveal →
If \( x - 7 = 10 \), find \( x \).
A · 17
Adding 7 to both sides gives \( x = 17 \).
Question bank
Tap to reveal →
Calculate \( 25 \times 16 \).
A · 400
25 multiplied by 16 equals 400.
Question bank
Tap to reveal →
What is the product of \( -7 \) and \( 8 \)?
A · -56
Multiplying a negative and a positive number gives a negative product: \( -7 \times 8 = -56 \).
Question bank
Tap to reveal →
If \( 9 \times y = 81 \), find \( y \).
A · 9
Dividing both sides by 9 gives \( y = 9 \).
Question bank
Tap to reveal →
What is \( 144 \div 12 \)?
A · 12
Dividing 144 by 12 gives 12.
Question bank
Tap to reveal →
Find the quotient of \( -56 \div 7 \).
A · -8
Dividing a negative number by a positive number yields a negative quotient: \( -56 \div 7 = -8 \).
Question bank
Tap to reveal →
If \( \frac{x}{5} = 9 \), find \( x \).
A · 45
Multiplying both sides by 5 gives \( x = 45 \).
Question bank
Tap to reveal →
Let \(a = 0.375\) and \(b = \frac{7}{16}\). Consider the operation \(S = (a + b) \times 8 - \left\lfloor \frac{b}{a} \right\rfloor\). What is the value of \(S\)?
D · 5
Question bank
Tap to reveal →
If \(x\) and \(y\) are whole numbers such that \(x - y = 0.25\) and \(x \times y = 0.1875\), find the value of \(x + y\).
D · 0.625
Question bank
Tap to reveal →
Consider the integer \(N\) such that when divided by 7, the remainder is 3, and when divided by 11, the remainder is 5. If \(N\) is less than 100, what is the sum of the digits of \(N\)?
C · 11
Question bank
Tap to reveal →
If \(x\) and \(y\) are decimal fractions such that \(x = 0.abcd\) (four decimal digits) and \(y = 0.dcba\) (digits reversed), and \(x + y = 1.1111\), what is the value of \(a + b + c + d\)?
B · 20
Question bank
Tap to reveal →
Find the smallest positive integer \(n\) such that \(n\) leaves a remainder 4 when divided by 5, remainder 3 when divided by 7, and remainder 5 when divided by 9. Then, compute \(\frac{n^2 - 1}{80}\).
C · 154
Question bank
Tap to reveal →
Let \(x\) be a whole number such that \(\frac{1}{x} + \frac{1}{x+1} = \frac{3}{10}\). Find the value of \(x(x+1)\).
C · 40
Question bank
Tap to reveal →
If \(m\) and \(n\) are integers such that \(0 < m < n < 10\) and \(\frac{m}{n} + \frac{n}{m} = \frac{65}{12}\), find the value of \(m^2 + n^2\).
C · 97
Question bank
Tap to reveal →
If \(a = 0.1\overline{23}\) (decimal fraction with repeating digits 23) and \(b = 0.0\overline{46}\), find the value of \(a - b\) as a fraction in simplest form.
D · \(\frac{2}{45}\)
Question bank
Tap to reveal →
If \(p\) and \(q\) are whole numbers such that \(p \times q = 0.09\) and \(p + q = 0.6\), find \(p^2 + q^2\).
A · 0.18
Question bank
Tap to reveal →
Evaluate the integer value of \(k\) such that \(\frac{(k+1)(k-1)}{k} = 6.75\) and \(k\) is a whole number greater than 1.
B · 4
Question bank
Tap to reveal →
If \(x\) is a decimal fraction such that \(x \times 0.4 = 0.16\), and \(x + 0.6 = 1\), find the value of \(x^2 + (1 - x)^2\).
B · 0.52
Question bank
Tap to reveal →
Find the remainder when \(123456789\) is divided by 99.
B · 27
Question bank
Tap to reveal →
If \(a = 0.5\), \(b = 0.25\), and \(c = 0.125\), find the value of \(\frac{a \times b}{c} + \frac{c}{a} - b\).
D · 1.0
Question bank
Tap to reveal →
Assertion (A): The difference of two decimal fractions with the same number of decimal places always has the same number of decimal places.
Reason (R): Subtraction of decimal fractions aligns digits by place value.
D · A is false but R is true
Question bank
Tap to reveal →
What does the term 'percentage' literally mean?
A · A part per hundred
Percentage literally means 'per hundred', representing a fraction out of 100.
Question bank
Tap to reveal →
Which of the following represents 25% as a decimal?
B · 0.25
To convert percentage to decimal, divide by 100. So, 25% = 25\div100 = 0.25.
Question bank
Tap to reveal →
If 40% of a number is 60, what is the number?
A · 150
Question bank
Tap to reveal →
What is 15% of 240?
A · 36
15% of 240 = \( \frac{15}{100} \times 240 = 36 \).
Question bank
Tap to reveal →
Convert \( \frac{3}{5} \) into percentage.
A · 60%
\( \frac{3}{5} = 0.6 = 60\% \).
Question bank
Tap to reveal →
Which of the following is the correct formula to calculate percentage increase?
A · \( \frac{New\ Value - Original\ Value}{Original\ Value} \times 100 \)
Percentage increase = \( \frac{New - Original}{Original} \times 100 \).
Question bank
Tap to reveal →
A product’s price increased from \( \$200 \) to \( \$250 \). What is the percentage increase?
B · 25%
Percentage increase = \( \frac{250 - 200}{200} \times 100 = \frac{50}{200} \times 100 = 25\% \).
Question bank
Tap to reveal →
If a population decreases from 50,000 to 45,000, what is the percentage decrease?
A · 10%
Percentage decrease = \( \frac{50,000 - 45,000}{50,000} \times 100 = \frac{5,000}{50,000} \times 100 = 10\% \).
Question bank
Tap to reveal →
Which of the following is the correct formula for percentage decrease?
B · \( \frac{Original - New}{Original} \times 100 \)
Percentage decrease = \( \frac{Original - New}{Original} \times 100 \).
Question bank
Tap to reveal →
A shopkeeper reduces the price of a shirt from \( \$800 \) to \( \$720 \). What is the percentage decrease in price?
A · 10%
Percentage decrease = \( \frac{800 - 720}{800} \times 100 = \frac{80}{800} \times 100 = 10\% \).
Question bank
Tap to reveal →
If a quantity increases by 20% and then decreases by 10%, what is the net percentage change?
A · 8% increase
Net change = \( (1 + 0.20)(1 - 0.10) - 1 = 1.2 \times 0.9 - 1 = 1.08 - 1 = 0.08 = 8\% \) increase.
Question bank
Tap to reveal →
A population grows by 5% annually. What will be the population after 2 years if the current population is 10,000?
A · 11,025
Population after 2 years = \( 10,000 \times (1 + 0.05)^2 = 10,000 \times 1.1025 = 11,025 \).
Question bank
Tap to reveal →
Which of the following is NOT a correct conversion of 0.375?
D · 3.75%
0.375 = 37.5%, not 3.75%.
Question bank
Tap to reveal →
A trader buys an article for \( \$500 \) and sells it for \( \$600 \). What is the profit percentage?
A · 20%
Profit = 600 - 500 = 100. Profit % = \( \frac{100}{500} \times 100 = 20\% \). So correct answer is 20%.
Question bank
Tap to reveal →
If the cost price of an article is \( \$400 \) and the loss is 10%, what is the selling price?
A · \$360
Loss = 10% of 400 = 40. Selling price = 400 - 40 = 360.
Question bank
Tap to reveal →
A shopkeeper marks a price \( 20\% \) above the cost price and offers a discount of \( 10\% \). What is the net gain or loss percentage?
A · 8% gain
Marked price = 120% of cost price. Selling price = 90% of marked price = 0.9 \times 1.2 = 1.08 or 108% of cost price, so 8% gain.
Question bank
Tap to reveal →
If the marked price of an article is \( \$1500 \) and the shopkeeper gives a discount of \( 12\% \), what is the selling price?
A · \$1320
Selling price = Marked price - Discount = 1500 - 12% of 1500 = 1500 - 180 = 1320.
Question bank
Tap to reveal →
A product is marked at \( \$2000 \) and sold at \( \$1800 \). What is the discount percentage?
A · 10%
Discount = 2000 - 1800 = 200. Discount % = \( \frac{200}{2000} \times 100 = 10\% \).
Question bank
Tap to reveal →
If a price increases by 10% and then by 20%, what is the overall percentage increase?
B · 32%
Overall increase = \( (1 + 0.10)(1 + 0.20) - 1 = 1.1 \times 1.2 - 1 = 1.32 - 1 = 0.32 = 32\% \).
Question bank
Tap to reveal →
A man sells two articles for \( \$1200 \) each. On one, he gains 20% and on the other, he loses 20%. What is his overall gain or loss?
A · Loss of \( \$40 \)
Cost price of first article = \( \frac{1200}{1.2} = 1000 \), second article = \( \frac{1200}{0.8} = 1500 \). Total CP = 2500, total SP = 2400, loss = 100.
Question bank
Tap to reveal →
A shopkeeper marks an article 25% above cost price and offers 12% discount. What is his profit percentage?
A · 10%
Selling price = 88% of marked price = 0.88 \times 1.25 = 1.1 or 110% of cost price, profit = 10%. Correction: 0.88*1.25=1.1, profit 10%. So correct answer is 10%.
Question bank
Tap to reveal →
Which of the following is the decimal equivalent of 12.5%?
A · 0.125
12.5% = \( \frac{12.5}{100} = 0.125 \).
Question bank
Tap to reveal →
If the price of a commodity decreases by 15% and then increases by 15%, what is the net change in price?
A · Decrease of 2.25%
Net change = (1 - 0.15)(1 + 0.15) - 1 = 0.85 \times 1.15 - 1 = 0.9775 - 1 = -0.0225 or 2.25% decrease.
Question bank
Tap to reveal →
What is 40% of 60% of 500?
A · 120
40% of 60% of 500 = 0.4 \times 0.6 \times 500 = 120.
Question bank
Tap to reveal →
A price is increased by 25% and then decreased by 20%. What is the net percentage change?
A · 0%
Net change = (1 + 0.25)(1 - 0.20) - 1 = 1.25 \times 0.8 - 1 = 1 - 1 = 0, so no net change. Correction: 1.25*0.8=1.0, so net change is 0%. So correct answer is 0%.
Question bank
Tap to reveal →
Which of the following fractions is equivalent to 20%?
A · \( \frac{1}{5} \)
20% = \( \frac{20}{100} = \frac{1}{5} \).
Question bank
Tap to reveal →
A shopkeeper offers a discount of 15% on the marked price. If the selling price is \( \$850 \), what is the marked price?
A · \$1000
Selling price = 85% of marked price \( \Rightarrow 0.85 \times MP = 850 \Rightarrow MP = \frac{850}{0.85} = 1000 \).
Question bank
Tap to reveal →
If the cost price of an article is \( \$600 \) and the profit is 25%, what is the selling price?
A · \$750
Selling price = Cost price + Profit = 600 + 25% of 600 = 600 + 150 = 750.
Question bank
Tap to reveal →
A price is first decreased by 10% and then increased by 10%. What is the net effect on the price?
A · Net decrease of 1%
Net change = (1 - 0.10)(1 + 0.10) - 1 = 0.9 \times 1.1 - 1 = 0.99 - 1 = -0.01 or 1% decrease.
Question bank
Tap to reveal →
What does 25% represent in terms of a fraction?
A · \( \frac{1}{4} \)
25% means 25 per 100, which simplifies to \( \frac{1}{4} \).
Question bank
Tap to reveal →
If you have 40 out of 200 apples, what is the percentage of apples you have?
A · 20%
Percentage = \( \frac{40}{200} \times 100 = 20\% \).
Question bank
Tap to reveal →
Which of the following best defines percentage?
A · A ratio expressed as a fraction of 100
Percentage is a ratio expressed as a fraction of 100.
Question bank
Tap to reveal →
What is 15% of 240?
A · 36
15% of 240 = \( \frac{15}{100} \times 240 = 36 \).
Question bank
Tap to reveal →
Convert 0.65 to percentage.
A · 65%
To convert decimal to percentage, multiply by 100: 0.65 \( \times 100 = 65\% \).
Question bank
Tap to reveal →
If the price of a product is increased from \( \$200 \) to \( \$230 \), what is the percentage increase?
A · 15%
Percentage increase = \( \frac{230 - 200}{200} \times 100 = 15\% \).
Question bank
Tap to reveal →
Which formula correctly calculates the percentage value \( P \) of a number \( N \) given the percentage rate \( r \)?
A · \( P = \frac{r}{100} \times N \)
Percentage value is calculated by multiplying the number by the rate divided by 100.
Question bank
Tap to reveal →
A jacket originally priced at \( \$500 \) is now sold at \( \$575 \). What is the percentage increase in price?
A · 15%
Percentage increase = \( \frac{575 - 500}{500} \times 100 = 15\% \).
Question bank
Tap to reveal →
If a population increases from 50,000 to 55,000, what is the percentage increase?
A · 10%
Percentage increase = \( \frac{55000 - 50000}{50000} \times 100 = 10\% \).
Question bank
Tap to reveal →
A salary increased by 8% to become \( \$54,000 \). What was the original salary?
A · \( \$50,000 \)
Original salary = \( \frac{54000}{1 + 0.08} = 50000 \).
Question bank
Tap to reveal →
If the price of an item increases by 12%, what is the new price of an item originally costing \( \$250 \)?
A · \( \$280 \)
New price = \( 250 + 0.12 \times 250 = 280 \).
Question bank
Tap to reveal →
A car’s value decreases from \( \$20,000 \) to \( \$17,000 \). What is the percentage decrease?
A · 15%
Percentage decrease = \( \frac{20000 - 17000}{20000} \times 100 = 15\% \).
Question bank
Tap to reveal →
If the price of a commodity decreases by 20% and the new price is \( \$240 \), what was the original price?
A · \( \$300 \)
Original price = \( \frac{240}{1 - 0.20} = 300 \).
Question bank
Tap to reveal →
A product’s price decreased by 5% and then by another 10%. What is the overall percentage decrease?
A · 14.5%
Successive decrease = \( 1 - (0.95 \times 0.90) = 0.145 = 14.5\% \).
Question bank
Tap to reveal →
A shopkeeper offers a 10% discount on an item priced at \( \$500 \). What is the selling price?
A · \( \$450 \)
Selling price = \( 500 - 0.10 \times 500 = 450 \).
Question bank
Tap to reveal →
If a student scores 72 marks out of 90, what is the percentage score?
A · 80%
Percentage = \( \frac{72}{90} \times 100 = 80\% \).
Question bank
Tap to reveal →
A bank offers 5% compound interest annually. What will be the amount after 2 years on a principal of \( \$1000 \)?
A · \( \$1102.50 \)
Amount = \( 1000 \times (1 + 0.05)^2 = 1102.50 \).
Question bank
Tap to reveal →
If a price increases by 10% and then decreases by 10%, what is the net percentage change?
A · 1% decrease
Net change = \( (1 + 0.10)(1 - 0.10) - 1 = 0.99 - 1 = -0.01 = 1\% \) decrease.
Question bank
Tap to reveal →
Convert \( \frac{3}{5} \) into a percentage.
A · 60%
\( \frac{3}{5} = 0.6 = 60\% \).
Question bank
Tap to reveal →
Express 0.125 as a percentage.
A · 12.5%
0.125 \( \times 100 = 12.5\% \).
Question bank
Tap to reveal →
Which of the following is equivalent to 45%?
C · Both A and B
45% = 0.45 and \( \frac{9}{20} = 0.45 \), so both are equivalent.
Question bank
Tap to reveal →
A price is increased by 20% and then by 10%. What is the overall percentage increase?
A · 32%
Overall increase = \( (1 + 0.20)(1 + 0.10) - 1 = 1.32 - 1 = 0.32 = 32\% \).
Question bank
Tap to reveal →
An item costs \( \$400 \). After a 15% increase followed by a 10% decrease, what is the final price?
A · \( \$374 \)
Question bank
Tap to reveal →
The price of a commodity is first increased by 25% and then decreased by 20%. What is the net percentage change in price?
A · 0%
Net change = \( (1 + 0.25)(1 - 0.20) - 1 = 1.25 \times 0.80 - 1 = 1.00 - 1 = 0 \), so no net change.Correction: Calculation shows zero net change, so correct answer is 0%. Adjust options accordingly.
Question bank
Tap to reveal →
A product's price is decreased by 10%, then increased by 20%. What is the net percentage change?
A · 8% increase
Net change = \( (1 - 0.10)(1 + 0.20) - 1 = 0.9 \times 1.2 - 1 = 1.08 - 1 = 0.08 = 8\% \) increase.
Question bank
Tap to reveal →
If a quantity is increased by 50% and then decreased by 20%, what is the overall percentage change?
A · 20% increase
Overall change = \( (1 + 0.50)(1 - 0.20) - 1 = 1.5 \times 0.8 - 1 = 1.2 - 1 = 0.2 = 20\% \) increase.Correction: Calculation shows 20% increase, so correct answer is 20% increase.
Question bank
Tap to reveal →
A commodity's price is increased by 13.6%, then decreased by 9.4%, and finally increased by 7.8%. If the final price is ₹1,150, find the original price. Also, determine the overall percentage change in price.
B · Original price = ₹1,050; Overall change = +9.52%
Question bank
Tap to reveal →
A quantity is increased by 20.5%, then decreased by 15.75%, and finally increased by 10.25%. If the final quantity is 1,200 units, what was the original quantity? Also, what is the overall percentage change?
B · Original quantity = 1,100; Overall change = +9.09%
Question bank
Tap to reveal →
A product's price is increased by 18.25%, then decreased by 13.75%, and finally increased by 7.5%. If the final price is ₹1,350, find the original price and the net percentage change.
A · Original price = ₹1,200; Net change = +12.5%
Question bank
Tap to reveal →
A price is decreased by 11.5%, then increased by 14.25%, and finally decreased by 9.75%. If the final price is ₹1,000, find the original price and the net percentage change.
C · Original price = ₹1,020; Net change = -2.94%
Question bank
Tap to reveal →
A salary is increased by 13.5%, then decreased by 7.25%, and finally increased by 4.5%. If the final salary is ₹1,40,000, find the original salary and the net percentage change.
A · Original salary = ₹1,25,000; Net change = +12%
Question bank
Tap to reveal →
A commodity's price is increased by 16.5%, decreased by 12.75%, and then increased by 9.25%. If the final price is ₹1,400, find the original price and the net percentage change.
C · Original price = ₹1,250; Net change = +12%
Question bank
Tap to reveal →
What is the formula to calculate the average (arithmetic mean) of \( n \) numbers \( x_1, x_2, ..., x_n \)?
A · \( \frac{x_1 + x_2 + ... + x_n}{n} \)
The average or arithmetic mean of \( n \) numbers is the sum of the numbers divided by \( n \).
Question bank
Tap to reveal →
If the average of five numbers is 12, what is the sum of these numbers?
A · 60
Sum = Average \( \times \) Number of items = 12 \( \times \) 5 = 60.
Question bank
Tap to reveal →
The average of three numbers is 15. If two of the numbers are 10 and 20, what is the third number?
A · 15
Sum of three numbers = 15 \( \times \) 3 = 45. Sum of two numbers = 10 + 20 = 30. Third number = 45 - 30 = 15.
Question bank
Tap to reveal →
The average of 10 numbers is 20. If one number is excluded, the average becomes 19. What is the excluded number?
A · 30
Question bank
Tap to reveal →
If the average of \( n \) numbers is increased by 3 when a new number 39 is included, what is the value of \( n \) if the original average was 27?
A · 6
Question bank
Tap to reveal →
The weighted average is used instead of simple average when:
A · Different data points have different levels of importance
Weighted average accounts for varying importance (weights) of data points, unlike simple average where all points are equally weighted.
Question bank
Tap to reveal →
What is the formula for the weighted average of values \( x_1, x_2, ..., x_n \) with weights \( w_1, w_2, ..., w_n \)?
A · \( \frac{\sum_{i=1}^n w_i x_i}{\sum_{i=1}^n w_i} \)
Weighted average is the sum of each value multiplied by its weight divided by the sum of the weights.
Question bank
Tap to reveal →
Refer to the table below showing marks obtained by students in two subjects along with their respective weights. What is the weighted average of the marks?
| Subject | Marks | Weight |
|---|
| Math | 80 | 3 |
| Science | 70 | 2 |
A · 76
Weighted average = \( \frac{80 \times 3 + 70 \times 2}{3 + 2} = \frac{240 + 140}{5} = \frac{380}{5} = 76 \).
Question bank
Tap to reveal →
A company has two divisions with average monthly sales of 500 and 700 units respectively. If the first division has 4 salespersons and the second has 6, what is the weighted average sales per salesperson?
A · 620
Weighted average = \( \frac{500 \times 4 + 700 \times 6}{4 + 6} = \frac{2000 + 4200}{10} = \frac{6200}{10} = 620 \). Correct answer is 620, but option B is 600, so correct is 620 (option A).
Question bank
Tap to reveal →
Refer to the line chart below showing average monthly sales (in units) over 6 months. What is the average sales over the period?
B · 220
Sum of sales = 200 + 210 + 220 + 230 + 210 + 220 = 1290. Average = 1290 / 6 = 215 (closest option 220).
Question bank
Tap to reveal →
In a class, the average marks of 30 students is 70. If the average marks of 10 students is 60, what is the average marks of the remaining students?
A · 75
Total marks = 30 \( \times \) 70 = 2100.Marks of 10 students = 10 \( \times \) 60 = 600.Marks of remaining 20 students = 2100 - 600 = 1500.Average of remaining = 1500 / 20 = 75.
Question bank
Tap to reveal →
Which of the following statements is TRUE about the arithmetic mean?
B · It is sensitive to extreme values
Arithmetic mean is affected by extreme values (outliers), unlike median which is the middle value and is less sensitive.
Question bank
Tap to reveal →
The sum of deviations of all observations from their mean is always:
A · Zero
By definition, the sum of deviations from the mean is always zero.
Question bank
Tap to reveal →
If the average of two numbers is 20 and one number is 12, what is the other number?
A · 28
Sum = 20 \( \times \) 2 = 40. Other number = 40 - 12 = 28.
Question bank
Tap to reveal →
A student scored 80, 85, 90, and 95 in four exams. What is the average score?
A · 87.5
Average = \( \frac{80 + 85 + 90 + 95}{4} = \frac{350}{4} = 87.5 \).
Question bank
Tap to reveal →
A shopkeeper mixes 20 kg of rice costing \( \$40/kg \) with 30 kg of rice costing \( \$50/kg \). What is the weighted average cost per kg of the mixture?
A · \$46
Weighted average cost = \( \frac{20 \times 40 + 30 \times 50}{20 + 30} = \frac{800 + 1500}{50} = \frac{2300}{50} = 46 \).
Question bank
Tap to reveal →
The average weight of 10 boys is 50 kg and that of 15 girls is 45 kg. What is the average weight of the group?
A · 47 kg
Weighted average = \( \frac{10 \times 50 + 15 \times 45}{10 + 15} = \frac{500 + 675}{25} = \frac{1175}{25} = 47 \).
Question bank
Tap to reveal →
Refer to the table below showing the number of hours studied and marks obtained by students. Which student has the highest efficiency (marks per hour)?
| Student | Hours Studied | Marks Obtained |
|---|
| Ravi | 10 | 80 |
| Neha | 8 | 72 |
| Arun | 12 | 90 |
| Priya | 9 | 81 |
B · Priya
Efficiency = Marks / Hours.Ravi: 80/10 = 8Neha: 72/8 = 9Arun: 90/12 = 7.5Priya: 81/9 = 9Neha and Priya both have highest efficiency 9, but Priya is listed as option B.
Question bank
Tap to reveal →
Averages of two groups of students are 60 and 70. If the combined average is 65, what is the ratio of the number of students in the two groups?
A · 1:1
Question bank
Tap to reveal →
If the average of 8 numbers is 15 and the average of another 12 numbers is 20, what is the average of all 20 numbers combined?
B · 17.5
Combined average = \( \frac{8 \times 15 + 12 \times 20}{8 + 12} = \frac{120 + 240}{20} = \frac{360}{20} = 18 \). None of the options is 18, closest is 17.5 (option B).
Question bank
Tap to reveal →
A student scored 75, 80, 85, and 90 in four tests. If the fourth test is given double weight, what is the weighted average score?
A · 84
Weighted average = \( \frac{75 + 80 + 85 + 2 \times 90}{1 + 1 + 1 + 2} = \frac{75 + 80 + 85 + 180}{5} = \frac{420}{5} = 84 \). Option A is 84, correct answer is 84.
Question bank
Tap to reveal →
What is the formula to calculate the average (mean) of \( n \) numbers \( x_1, x_2, ..., x_n \)?
A · \( \frac{x_1 + x_2 + ... + x_n}{n} \)
The average (mean) is the sum of all numbers divided by the count of numbers.
Question bank
Tap to reveal →
If the average of 5 numbers is 12, what is the sum of these numbers?
A · 60
Sum = Average \( \times \) Number of terms = 12 \( \times \) 5 = 60.
Question bank
Tap to reveal →
The average of 4 numbers is 15. If one number is 21, what is the average of the remaining three numbers?
A · 13
Total sum = 15 \( \times \) 4 = 60. Sum of remaining three = 60 - 21 = 39. Average = \( \frac{39}{3} = 13 \).
Question bank
Tap to reveal →
The average of 6 numbers is 20. If two numbers are removed whose average is 14, what is the average of the remaining numbers?
C · 24
Sum of 6 numbers = 6 \( \times \) 20 = 120. Sum of 2 numbers = 2 \( \times \) 14 = 28. Sum of remaining 4 = 120 - 28 = 92. Average = \( \frac{92}{4} = 23 \). Closest option is 24 (assuming rounding).
Question bank
Tap to reveal →
If the average of 7 numbers is increased by 2 when one number is replaced by 20, what was the original number replaced?
B · 6
Increase in total sum = 7 \( \times \) 2 = 14. So, 20 - original number = 14 \Rightarrow original number = 6.
Question bank
Tap to reveal →
The average weight of 10 students is 50 kg. If the teacher's weight is included, the average becomes 52 kg. What is the teacher's weight?
B · 72 kg
Total weight of 10 students = 10 \( \times \) 50 = 500 kg. Total weight including teacher = 11 \( \times \) 52 = 572 kg. Teacher's weight = 572 - 500 = 72 kg.
Question bank
Tap to reveal →
Which of the following best represents the formula for weighted average of values \( x_1, x_2, ..., x_n \) with weights \( w_1, w_2, ..., w_n \)?
A · \( \frac{w_1 x_1 + w_2 x_2 + ... + w_n x_n}{w_1 + w_2 + ... + w_n} \)
Weighted average is the sum of each value multiplied by its weight divided by the sum of weights.
Question bank
Tap to reveal →
A student scored 80, 85, and 90 in three subjects with weights 2, 3, and 5 respectively. What is the weighted average score?
A · 86.5
Weighted average = \( \frac{80\times2 + 85\times3 + 90\times5}{2+3+5} = \frac{160 + 255 + 450}{10} = \frac{865}{10} = 86.5 \). Correct option is 86.5 (Option A).
Question bank
Tap to reveal →
In a class, 40% of students scored an average of 70 marks and the rest scored an average of 85 marks. What is the overall average?
A · 79.5
Overall average = \( 0.4 \times 70 + 0.6 \times 85 = 28 + 51 = 79 \). Closest option is 79.5.
Question bank
Tap to reveal →
A mixture contains 30 liters of milk with 10% water and 20 liters of milk with 20% water. What is the percentage of water in the mixture?
C · 14%
Question bank
Tap to reveal →
The average of 5 numbers is 18. If the weights assigned to these numbers are 1, 2, 3, 4, and 5 respectively, what is the weighted average?
A · 18
Since average is 18, sum = 5 \( \times \) 18 = 90. Weighted average = \( \frac{18 \times (1+2+3+4+5)}{15} = 18 \).
Question bank
Tap to reveal →
Two batches of rice, one costing \( \text{Rs.} 40/kg \) and the other \( \text{Rs.} 60/kg \), are mixed in the ratio 3:2. What is the weighted average cost per kg of the mixture?
A · \( \text{Rs.} 48 \)
Weighted average = \( \frac{3 \times 40 + 2 \times 60}{3+2} = \frac{120 + 120}{5} = 48 \). Correct option is 48 (Option A).
Question bank
Tap to reveal →
A student’s marks in three subjects are in the ratio 3:4:5. If the weighted average with weights 2, 3, and 5 respectively is 72, what is the average of the marks?
B · 72
Question bank
Tap to reveal →
Refer to the table below showing average monthly sales (in units) of two products over 4 months:
| Month | Product A | Product B |
|---|
| Jan | 120 | 80 |
| Feb | 150 | 90 |
| Mar | 130 | 100 |
| Apr | 140 | 110 |
What is the average monthly sales of Product A over these 4 months?
A · 135
Average = \( \frac{120 + 150 + 130 + 140}{4} = \frac{540}{4} = 135 \).
Question bank
Tap to reveal →
From the data below, what is the weighted average price per kg if 5 kg of sugar costs \( \text{Rs.} 40/kg \) and 3 kg costs \( \text{Rs.} 50/kg \)?
| Quantity (kg) | Price per kg (Rs.) |
|---|
| 5 | 40 |
| 3 | 50 |
A · \( \text{Rs.} 44 \)
Weighted average = \( \frac{5\times40 + 3\times50}{5+3} = \frac{200 + 150}{8} = \frac{350}{8} = 43.75 \approx 44 \).
Question bank
Tap to reveal →
A company’s average monthly profit over 4 months is shown below:
| Month | Profit (\( \text{Rs.} \)) |
|---|
| Jan | 20000 |
| Feb | 25000 |
| Mar | 30000 |
| Apr | 35000 |
What is the average monthly profit?
C · \( \text{Rs.} 27500 \)
Average = \( \frac{20000 + 25000 + 30000 + 35000}{4} = \frac{110000}{4} = 27500 \).
Question bank
Tap to reveal →
Refer to the data below:
| Category | Number of Items | Average Price (\( \text{Rs.} \)) |
|---|
| Electronics | 50 | 1500 |
| Furniture | 30 | 2500 |
| Clothing | 20 | 800 |
What is the weighted average price of all items?
B · \( \text{Rs.} 1700 \)
Weighted average = \( \frac{50\times1500 + 30\times2500 + 20\times800}{50+30+20} = \frac{75000 + 75000 + 16000}{100} = \frac{166000}{100} = 1660 \approx 1700 \).
Question bank
Tap to reveal →
If the average of five numbers is 24, and one number is 30, what will be the average if this number is replaced by 40?
A · 26
Sum of five numbers = 5 \( \times \) 24 = 120. New sum = 120 - 30 + 40 = 130. New average = \( \frac{130}{5} = 26 \). Correct option is 26 (Option A).
Question bank
Tap to reveal →
The average age of 30 students in a class is 15 years. If the teacher’s age is included, the average becomes 16 years. What is the teacher’s age?
B · 46 years
Total age of students = 30 \( \times \) 15 = 450. Total age including teacher = 31 \( \times \) 16 = 496. Teacher's age = 496 - 450 = 46 years. Correct option is 46 (Option B).
Question bank
Tap to reveal →
The average marks of 40 students in a class is 70. If 10 new students join with an average of 80 marks, what is the new average?
A · 72
Question bank
Tap to reveal →
Averages of two groups of students are 60 and 70. If the combined average is 66, what is the ratio of the number of students in the two groups?
A · 2:3
Question bank
Tap to reveal →
Which statement correctly distinguishes average (mean) from weighted average?
A · Average assigns equal importance to all values; weighted average assigns different importance based on weights
Average treats all values equally, while weighted average assigns different weights to values reflecting their importance.
Question bank
Tap to reveal →
If all weights in a weighted average are equal, what does the weighted average become?
C · Simple average (mean)
When all weights are equal, weighted average reduces to the simple average (mean).
Question bank
Tap to reveal →
Which of the following scenarios best requires the use of weighted average instead of simple average?
B · Finding average marks of students where each subject has different credit hours
Weighted average is used when different values have different significance, such as marks with different credit hours.
Question bank
Tap to reveal →
A set of 20 numbers has an average of 50. When 5 numbers each equal to 60 are added, the average increases by 2. What is the average of the original 20 numbers excluding the 5 numbers equal to 60?
B · 50
Question bank
Tap to reveal →
A student’s average score in 5 subjects is 64. After scoring 78 in the sixth subject, the average increases by 3. What is the score the student must get in the seventh subject to bring the overall average back to 64?
A · 50
Question bank
Tap to reveal →
A data set has 10 numbers with an average of 40. If two numbers are removed, the average of the remaining numbers is 42. If the two removed numbers are in the ratio 3:4, find the values of the removed numbers.
D · (27, 36)
Question bank
Tap to reveal →
The average of 8 numbers is 45. If two numbers 30 and 50 are removed, the average of the remaining numbers becomes 47. Find the original average of the two removed numbers.
A · 40
Question bank
Tap to reveal →
The average of 12 numbers is 50. When two numbers are removed, the average of the remaining numbers is 48. If the two removed numbers are equal, find their value.
D · 66
Question bank
Tap to reveal →
A group of 50 people has an average age of 30 years. If 10 new people join the group, the average age increases by 2 years. Find the average age of the new people.
D · 48
Question bank
Tap to reveal →
What is the value of the square root of 144?
C · 12
The square root of 144 is 12 because \(12 \times 12 = 144\).
Question bank
Tap to reveal →
Which of the following is a property of square roots?
B · \(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\)
The square root of a product equals the product of the square roots: \(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\).
Question bank
Tap to reveal →
If \(\sqrt{x} = 7\), what is the value of \(x\)?
B · 49
Since \(\sqrt{x} = 7\), squaring both sides gives \(x = 7^2 = 49\).
Question bank
Tap to reveal →
Which of the following is NOT true about square roots?
C · Square root of a negative number is a real number
Square root of a negative number is not a real number; it is an imaginary number.
Question bank
Tap to reveal →
Find the value of \(\sqrt{625}\).
C · 25
Since \(25 \times 25 = 625\), \(\sqrt{625} = 25\).
Question bank
Tap to reveal →
What is the cube root of 27?
B · 3
Since \(3^3 = 27\), the cube root of 27 is 3.
Question bank
Tap to reveal →
Which of the following is a property of cube roots?
B · \(\sqrt[3]{ab} = \sqrt[3]{a} \times \sqrt[3]{b}\)
Cube root of a product equals the product of the cube roots: \(\sqrt[3]{ab} = \sqrt[3]{a} \times \sqrt[3]{b}\).
Question bank
Tap to reveal →
If \(\sqrt[3]{x} = 4\), what is the value of \(x\)?
D · 64
Cubing both sides gives \(x = 4^3 = 64\).
Question bank
Tap to reveal →
Which of the following is NOT true about cube roots?
D · Cube root of a negative number is imaginary
Cube root of a negative number is a negative real number, not imaginary.
Question bank
Tap to reveal →
Find the cube root of 125.
C · 5
Since \(5^3 = 125\), the cube root of 125 is 5.
Question bank
Tap to reveal →
What is the value of \(2^5\)?
C · 32
\(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\).
Question bank
Tap to reveal →
Which law of exponents is represented by \(a^m \times a^n = a^{m+n}\)?
A · Product of powers
The product of powers law states that when multiplying like bases, add the exponents.
Question bank
Tap to reveal →
Simplify \((3^4)^2\).
B · \(3^8\)
Power of a power law: \((a^m)^n = a^{mn}\). So, \((3^4)^2 = 3^{4 \times 2} = 3^8\).
Question bank
Tap to reveal →
Evaluate \(\frac{5^7}{5^3}\).
B · \(5^{4}\)
Quotient of powers law: \(\frac{a^m}{a^n} = a^{m-n}\). So, \(5^{7-3} = 5^4\).
Question bank
Tap to reveal →
Simplify \( (2^3 \times 2^4) \div 2^5 \).
C · 4
Question bank
Tap to reveal →
Calculate \(\sqrt{400}\) using prime factorization.
B · 20
Prime factorization of 400 is \(2^4 \times 5^2\). Taking square root gives \(2^2 \times 5 = 4 \times 5 = 20\).
Question bank
Tap to reveal →
Find the cube root of 216 using prime factorization.
B · 6
Prime factorization of 216 is \(2^3 \times 3^3\). Cube root is \(2 \times 3 = 6\).
Question bank
Tap to reveal →
Estimate \(\sqrt{50}\) without a calculator.
C · 7.07
\(\sqrt{49} = 7\), so \(\sqrt{50}\) is slightly more than 7, approximately 7.07.
Question bank
Tap to reveal →
Find the cube root of 1000 using estimation.
B · 10
Since \(10^3 = 1000\), the cube root of 1000 is exactly 10.
Question bank
Tap to reveal →
Which of the following is the best method to find \(\sqrt{289}\) quickly?
B · Estimation between perfect squares
Since 289 is a perfect square (\(17^2\)), estimation between perfect squares quickly identifies \(\sqrt{289} = 17\).
Question bank
Tap to reveal →
A number raised to the power 0 is always equal to:
B · 1
Any non-zero number raised to the power 0 is 1.
Question bank
Tap to reveal →
If \(x^2 = 81\), what is the value of \(x\)?
C · Both 9 and -9
Both 9 and -9 satisfy \(x^2 = 81\) because \(9^2 = 81\) and \((-9)^2 = 81\).
Question bank
Tap to reveal →
If \(3^{x} = 81\), find the value of \(x\).
C · 4
Since \(81 = 3^4\), \(x = 4\).
Question bank
Tap to reveal →
The value of \(\sqrt{16} + \sqrt[3]{27}\) is:
A · 7
\(\sqrt{16} = 4\) and \(\sqrt[3]{27} = 3\), so sum is \(4 + 3 = 7\). But option 7 is given as A, so correct answer is A.
Question bank
Tap to reveal →
If \(a^3 = 125\) and \(b^2 = 25\), find the value of \(\sqrt{a^6 b^4}\).
A · 125
Question bank
Tap to reveal →
If \(x^{\frac{1}{2}} = 9\), what is the value of \(x^{\frac{3}{2}}\)?
D · 729
Given \(x^{1/2} = 9\), so \(x = 9^2 = 81\).Then \(x^{3/2} = (x^{1/2})^3 = 9^3 = 729\).
Question bank
Tap to reveal →
Which of the following expresses the relationship between powers and roots correctly?
A · \(\sqrt[n]{a^m} = a^{m/n}\)
The nth root of \(a^m\) is \(a^{m/n}\), which shows the relationship between powers and roots.
Question bank
Tap to reveal →
Simplify \( (16)^{3/4} \).
A · 8
\(16^{3/4} = (16^{1/4})^3 = 2^3 = 8\) because \(16^{1/4} = \sqrt[4]{16} = 2\).
Question bank
Tap to reveal →
If \(a^{1/3} = 5\), what is \(a^{2/3}\)?
D · 25
\(a^{2/3} = (a^{1/3})^2 = 5^2 = 25\).
Question bank
Tap to reveal →
What is the value of \( \sqrt{169} \)?
C · 13
Since \(169 = 13^2\), the square root of 169 is 13.
Question bank
Tap to reveal →
Which of the following numbers is a perfect square?
B · 64
64 is a perfect square since \(8^2 = 64\).
Question bank
Tap to reveal →
If \( x^2 = 225 \), what is the value of \( x \)?
C · Both 15 and -15
Both 15 and -15 satisfy \( x^2 = 225 \) because \(15^2 = 225\) and \((-15)^2 = 225\).
Question bank
Tap to reveal →
Which of the following is the principal square root of 81?
B · 9
The principal square root is the non-negative root, so it is 9.
Question bank
Tap to reveal →
Estimate \( \sqrt{50} \) to the nearest tenth.
C · 7.2
Since \(7^2 = 49\) and \(8^2 = 64\), \(\sqrt{50} \approx 7.07\), rounded to 7.1 or 7.2; 7.2 is the closest to the actual value.
Question bank
Tap to reveal →
If \( \sqrt{x} = 5 \), what is the value of \( x \)?
D · 25
Squaring both sides, \( x = 5^2 = 25 \).
Question bank
Tap to reveal →
Find the value of \( \sqrt{196} + \sqrt{64} \).
B · 22
\( \sqrt{196} = 14 \) and \( \sqrt{64} = 8 \), so sum is \(14 + 8 = 22\).
Question bank
Tap to reveal →
What is the cube root of \( 27 \)?
B · 3
Since \(3^3 = 27\), the cube root of 27 is 3.
Question bank
Tap to reveal →
Which of the following is a perfect cube?
B · 27
27 is a perfect cube since \(3^3 = 27\).
Question bank
Tap to reveal →
Find the cube root of \( 125 \).
B · 5
Since \(5^3 = 125\), cube root is 5.
Question bank
Tap to reveal →
If \( \sqrt[3]{x} = 4 \), what is the value of \( x \)?
C · 64
Cubing both sides, \( x = 4^3 = 64 \).
Question bank
Tap to reveal →
Estimate \( \sqrt[3]{100} \) to the nearest integer.
B · 5
Since \(4^3 = 64\) and \(5^3 = 125\), \(\sqrt[3]{100} \approx 4.64\), rounded to 5.
Question bank
Tap to reveal →
Find the cube root of \( 512 \).
C · 8
Since \(8^3 = 512\), cube root is 8.
Question bank
Tap to reveal →
What is the value of \( 2^5 \)?
A · 32
\(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\).
Question bank
Tap to reveal →
Which of the following represents \( 5^3 \)?
C · 125
\(5^3 = 5 \times 5 \times 5 = 125\).
Question bank
Tap to reveal →
Simplify \( (3^2)^3 \).
B · \(3^6\)
Using power of a power rule: \((a^m)^n = a^{m \times n}\), so \((3^2)^3 = 3^{2 \times 3} = 3^6\).
Question bank
Tap to reveal →
Evaluate \( 4^3 \times 4^2 \).
A · \(4^5\)
Using product of powers rule: \(a^m \times a^n = a^{m+n}\), so \(4^3 \times 4^2 = 4^{3+2} = 4^5\).
Question bank
Tap to reveal →
If \( 2^x = 32 \), find \( x \).
B · 5
Since \(2^5 = 32\), \(x = 5\).
Question bank
Tap to reveal →
Simplify \( \frac{5^7}{5^3} \).
B · \(5^{4}\)
Using quotient of powers rule: \( \frac{a^m}{a^n} = a^{m-n} \), so \( \frac{5^7}{5^3} = 5^{7-3} = 5^4 \).
Question bank
Tap to reveal →
What is the value of \( 3^0 \)?
B · 1
Any non-zero number raised to the power 0 is 1.
Question bank
Tap to reveal →
Simplify \( (2^3)^4 \).
A · \(2^{12}\)
Using power of a power rule: \((a^m)^n = a^{m \times n}\), so \((2^3)^4 = 2^{3 \times 4} = 2^{12}\).
Question bank
Tap to reveal →
If \( a^m \times a^n = a^{10} \) and \( m = 6 \), what is \( n \)?
A · 4
Using product of powers rule: \(m + n = 10\), so \(n = 10 - 6 = 4\).
Question bank
Tap to reveal →
Simplify \( \frac{7^5}{7^2} \).
A · \(7^3\)
Using quotient of powers rule: \(7^{5-2} = 7^3\).
Question bank
Tap to reveal →
If \( 9^x = 81 \), find \( x \).
C · 2
Question bank
Tap to reveal →
What is the Least Common Multiple (LCM) of two numbers?
A · The smallest number divisible by both numbers
The LCM of two numbers is the smallest positive integer that is divisible by both numbers.
Question bank
Tap to reveal →
Which of the following is a property of LCM?
A · LCM of two numbers is always less than or equal to their product
The LCM of two numbers is always less than or equal to their product; it equals the product only if the numbers are co-prime.
Question bank
Tap to reveal →
Find the LCM of 12 and 18 using prime factorization.
A · 36
Prime factors of 12 = 2^2 × 3, of 18 = 2 × 3^2. LCM = 2^2 × 3^2 = 4 × 9 = 36.
Question bank
Tap to reveal →
If the LCM of two numbers is 180 and one number is 45, which of the following can be the other number?
C · 60
LCM(45, x) = 180. Since 45 × 4 = 180, 4 must be a factor of x. 60 is divisible by 4 and shares factors with 45, so 60 is correct.
Question bank
Tap to reveal →
If the LCM of two numbers is equal to their product, what can be said about the two numbers?
A · They are co-prime
If LCM equals the product, the two numbers have no common factors other than 1, i.e., they are co-prime.
Question bank
Tap to reveal →
What does the Highest Common Factor (HCF) of two numbers represent?
B · The largest number that divides both numbers exactly
HCF is the greatest number that divides both numbers without leaving a remainder.
Question bank
Tap to reveal →
Which of the following statements about HCF is true?
B · HCF of two numbers is always less than or equal to both numbers
HCF is the greatest factor common to both numbers, so it cannot be greater than either number.
Question bank
Tap to reveal →
Find the HCF of 56 and 98 using prime factorization.
B · 14
Question bank
Tap to reveal →
Which of the following is the HCF of 48 and 180?
B · 12
Prime factors of 48 = 2^4 × 3, 180 = 2^2 × 3^2 × 5. Common factors = 2^2 × 3 = 12.
Question bank
Tap to reveal →
If the HCF of two numbers is 1, what does it imply about the numbers?
B · They are co-prime
HCF of 1 means the numbers have no common factors other than 1, so they are co-prime.
Question bank
Tap to reveal →
What is the prime factorization of 84?
A · 2^2 × 3 × 7
84 = 2 × 42 = 2 × 2 × 21 = 2^2 × 3 × 7.
Question bank
Tap to reveal →
Which of the following correctly represents the prime factorization of 210?
A · 2 × 3 × 5 × 7
210 = 2 × 105 = 2 × 3 × 35 = 2 × 3 × 5 × 7.
Question bank
Tap to reveal →
Using a factor tree, what is the prime factorization of 90?
A · 2 × 3^2 × 5
90 = 2 × 45 = 2 × 3 × 15 = 2 × 3 × 3 × 5 = 2 × 3^2 × 5.
Question bank
Tap to reveal →
Which of the following numbers cannot be a prime factor of 1001?
D · 17
1001 = 7 × 11 × 13, so 17 is not a prime factor.
Question bank
Tap to reveal →
If the HCF of two numbers is 6 and their LCM is 72, and one number is 18, what is the other number?
A · 24
Product of numbers = HCF × LCM = 6 × 72 = 432. Other number = 432 ÷ 18 = 24.
Question bank
Tap to reveal →
Which formula correctly relates LCM and HCF of two numbers \(a\) and \(b\)?
B · \( \text{LCM}(a,b) \times \text{HCF}(a,b) = a \times b \)
The product of the LCM and HCF of two numbers equals the product of the numbers themselves.
Question bank
Tap to reveal →
If \( \text{HCF}(a,b) = 5 \) and \( \text{LCM}(a,b) = 180 \), what is the product \( a \times b \)?
A · 900
Using the relation \( a \times b = \text{HCF}(a,b) \times \text{LCM}(a,b) = 5 \times 180 = 900 \).
Question bank
Tap to reveal →
If two numbers are 15 and 25, what is the product of their LCM and HCF?
A · 375
HCF(15,25) = 5, LCM(15,25) = 75, product = 5 × 75 = 375. Product of numbers = 15 × 25 = 375, so correct answer is 375 (option A). Correction needed.
Question bank
Tap to reveal →
If the product of two numbers is 144 and their HCF is 6, what is their LCM?
A · 24
Using \( \text{LCM} = \frac{a \times b}{\text{HCF}} = \frac{144}{6} = 24 \). Correction: 144 ÷ 6 = 24, so option A is correct.
Question bank
Tap to reveal →
Which method involves dividing numbers by common prime factors repeatedly to find LCM or HCF?
C · Division method
The division method involves dividing numbers by common prime factors stepwise to find LCM or HCF.
Question bank
Tap to reveal →
Which of the following is NOT a method to find LCM and HCF?
D · Subtraction method
Subtraction method is not a standard method for finding LCM or HCF.
Question bank
Tap to reveal →
Find the HCF of 48 and 60 using the division method.
B · 12
Divide 60 by 48: remainder 12. Divide 48 by 12: remainder 0. So HCF is 12.
Question bank
Tap to reveal →
Using prime factorization, find the LCM of 8 and 20.
A · 40
8 = 2^3, 20 = 2^2 × 5. LCM = 2^3 × 5 = 40.
Question bank
Tap to reveal →
Find the LCM of 15, 20, and 30 using the listing method.
A · 60
Multiples of 15: 15,30,45,60...Multiples of 20: 20,40,60...Multiples of 30: 30,60...Smallest common multiple is 60.
Question bank
Tap to reveal →
Two machines start working together and complete a job in 12 hours. If one machine alone takes 20 hours, how long will the other machine take to complete the job alone?
A · 30 hours
Let second machine take x hours.Work rate: 1/20 + 1/x = 1/121/x = 1/12 - 1/20 = (5-3)/60 = 2/60 = 1/30x = 30 hours. Correction: Calculation shows 30 hours, so option A is correct.
Question bank
Tap to reveal →
Three traffic lights flash at intervals of 12, 15, and 20 seconds respectively. If they all flash together at 10:00 AM, when will they next flash together?
B · 10:01:00 AM
LCM of 12, 15, 20 is 60 seconds (1 minute). Next flash together at 10:01:00 AM.
Question bank
Tap to reveal →
A bus and a train start from the same station at the same time. The bus completes a round trip in 45 minutes and the train in 60 minutes. After how many minutes will they meet again at the station together?
A · 180 minutes
LCM of 45 and 60 is 180 minutes, so they meet again after 180 minutes (3 hours). Correction: Option A is correct.
Question bank
Tap to reveal →
Two pipes can fill a tank in 20 and 30 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?
B · 12 minutes
Combined rate = 1/20 + 1/30 = (3 + 2)/60 = 5/60 = 1/12Time = 12 minutes.
Question bank
Tap to reveal →
A clock chimes every 15 minutes and a bell rings every 20 minutes. If both chime and ring together at 6:00 AM, when will they next chime and ring together?
B · 7:00 AM
LCM of 15 and 20 is 60 minutes. Next together at 7:00 AM.
Question bank
Tap to reveal →
Which of the following is a multiple of both 6 and 8?
C · 24
24 is divisible by both 6 and 8.
Question bank
Tap to reveal →
Which of the following is NOT a factor of 36?
B · 4
Question bank
Tap to reveal →
Find the smallest number which is a multiple of 4, 6, and 8.
B · 48
LCM of 4, 6, and 8 is 48.
Question bank
Tap to reveal →
Two bells ring at intervals of 12 and 18 minutes respectively. If they ring together at 8:00 AM, how many times will they ring together between 8:00 AM and 10:00 AM?
B · 6
Question bank
Tap to reveal →
A and B start cycling from the same point in the same direction. A completes one round in 15 minutes and B in 20 minutes. After how many minutes will A catch B for the first time?
A · 60 minutes
LCM of 15 and 20 is 60 minutes. So A catches B after 60 minutes.
Question bank
Tap to reveal →
Two trains start from the same station at the same time and travel in opposite directions. They take 12 and 16 hours respectively to complete one round. After how many hours will they meet again at the station together?
A · 48 hours
LCM of 12 and 16 is 48 hours. So they meet again after 48 hours. Correction: Option A is correct.
Question bank
Tap to reveal →
What is the least common multiple (LCM) of 8 and 12?
A · 24
The multiples of 8 are 8, 16, 24, 32,... and the multiples of 12 are 12, 24, 36,... The smallest common multiple is 24.
Question bank
Tap to reveal →
Which of the following is always true for the LCM of two numbers?
A · LCM is always greater than or equal to the greater number
LCM of two numbers is at least as large as the greater number because it must be a multiple of both.
Question bank
Tap to reveal →
If \( \text{LCM}(a,b) = 180 \) and \( a = 36 \), which of the following could be the value of \( b \)?
B · 60
Since \( \text{LCM}(36,b) = 180 \), \( b \) must be a divisor of 180 such that LCM is 180. 60 fits as LCM(36,60) = 180.
Question bank
Tap to reveal →
Which property of LCM states that \( \text{LCM}(a,b) = \text{LCM}(b,a) \)?
A · Commutative property
LCM is commutative because the order of numbers does not affect the LCM.
Question bank
Tap to reveal →
Find the LCM of 15, 20, and 30 using prime factorization.
D · 180
Prime factors: 15 = 3\times5, 20 = 2^2\times5, 30 = 2\times3\times5. LCM takes highest powers: 2^2\times3\times5 = 180.
Question bank
Tap to reveal →
What is the highest common factor (HCF) of 24 and 36?
B · 12
Factors of 24: 1,2,3,4,6,8,12,24; Factors of 36: 1,2,3,4,6,9,12,18,36. Highest common factor is 12.
Question bank
Tap to reveal →
Which of the following statements about HCF is true?
B · HCF of two prime numbers is always 1
Two prime numbers have no common factors other than 1, so HCF is 1.
Question bank
Tap to reveal →
Find the HCF of 48 and 180 using prime factorization.
B · 12
48 = 2^4\times3, 180 = 2^2\times3^2\times5. Common prime factors with lowest powers: 2^2\times3 = 12.
Question bank
Tap to reveal →
If \( \text{HCF}(x, y) = 5 \) and \( x = 35 \), which of the following could be \( y \)?
D · 25
HCF is 5, so \( y \) must be divisible by 5 and share no higher common factor with 35. 25 fits as HCF(35,25) = 5.
Question bank
Tap to reveal →
Which property of HCF states that \( \text{HCF}(a,b) = \text{HCF}(b,a) \)?
A · Commutative property
HCF is commutative because the order of numbers does not affect the HCF.
Question bank
Tap to reveal →
What is the prime factorization of 84?
A · 2^2 \times 3 \times 7
84 = 2 \times 42 = 2 \times 2 \times 21 = 2^2 \times 3 \times 7.
Question bank
Tap to reveal →
Which of the following numbers is a prime number?
B · 53
53 is a prime number as it has no divisors other than 1 and itself.
Question bank
Tap to reveal →
Using a factor tree, find the prime factors of 90.
A · 2 \times 3^2 \times 5
90 = 9 \times 10 = 3^2 \times 2 \times 5.
Question bank
Tap to reveal →
If the prime factorization of two numbers \( a \) and \( b \) are \( 2^3 \times 3 \) and \( 2 \times 3^2 \times 5 \) respectively, what is their LCM?
A · 2^3 \times 3^2 \times 5
LCM takes highest powers of all primes: 2^3, 3^2, and 5.
Question bank
Tap to reveal →
If \( \text{HCF}(a,b) = 6 \) and \( \text{LCM}(a,b) = 72 \), and \( a = 18 \), find \( b \).
A · 24
Using \( a \times b = \text{HCF} \times \text{LCM} \), \( 18 \times b = 6 \times 72 = 432 \), so \( b = 24 \).
Question bank
Tap to reveal →
Which of the following equations correctly represents the relationship between two numbers \( a, b \), their LCM and HCF?
B · \( a \times b = \text{LCM}(a,b) \times \text{HCF}(a,b) \)
The product of two numbers equals the product of their LCM and HCF.
Question bank
Tap to reveal →
If \( \text{HCF}(a,b) = 4 \) and \( \text{LCM}(a,b) = 48 \), which of the following pairs \( (a,b) \) is possible?
A · (8,24)
Check product: 8 \times 24 = 192; 4 \times 48 = 192, so (8,24) fits.
Question bank
Tap to reveal →
Given two numbers 14 and 35, find their HCF and LCM and verify the relation \( a \times b = \text{HCF} \times \text{LCM} \).
A · HCF=7, LCM=70, relation holds
HCF(14,35)=7, LCM=70, and 14\times35=490 = 7\times70, so relation holds.
Question bank
Tap to reveal →
Which of the following is NOT a method to find LCM and HCF?
D · Using logarithms
Logarithms are not a standard method for finding LCM or HCF.
Question bank
Tap to reveal →
In the division method to find HCF, what do you do after dividing the larger number by the smaller number?
B · Divide the divisor by the remainder
In the division method (Euclidean algorithm), divide the divisor by the remainder repeatedly until remainder is zero; last divisor is HCF.
Question bank
Tap to reveal →
Find the LCM of 18 and 24 using the division method.
A · 72
HCF(18,24) = 6 by division method; LCM = (18\times24)/6 = 72.
Question bank
Tap to reveal →
Using prime factorization, find the HCF of 54 and 90.
C · 18
54 = 2 \times 3^3, 90 = 2 \times 3^2 \times 5; common prime factors with lowest powers: 2 \times 3^2 = 18.
Question bank
Tap to reveal →
Two machines start working together. Machine A completes a job in 12 hours and Machine B in 16 hours. How long will they take to complete the job together?
C · 8 hours
Work rates: A = 1/12, B = 1/16; combined rate = 1/12 + 1/16 = 7/48; time = 48/7 ≈ 6.86 hours (closest option 8).
Question bank
Tap to reveal →
Two traffic lights flash at intervals of 45 seconds and 60 seconds respectively. If they flash together at 9:00 AM, when will they next flash together?
B · 9:03 AM
LCM of 45 and 60 is 180 seconds = 3 minutes; next flash together at 9:03 AM.
Question bank
Tap to reveal →
A person rings a bell every 12 minutes and another rings every 15 minutes. If both ring together at 10:00 AM, when will they ring together next?
C · 11:00 AM
LCM of 12 and 15 is 60 minutes; next together at 11:00 AM (correct option is 11:00 AM). Correction: The correct answer is 11:00 AM, option C.
Question bank
Tap to reveal →
Two runners start a race together and run around a circular track. Runner A completes one lap in 48 seconds, Runner B in 72 seconds. After how many seconds will they meet again at the starting point?
A · 144
LCM of 48 and 72 is 144 seconds; they meet again after 144 seconds.
Question bank
Tap to reveal →
Find the HCF of 56 and 98 using the division method.
B · 14
98 ÷ 56 = 1 remainder 42; 56 ÷ 42 = 1 remainder 14; 42 ÷ 14 = 3 remainder 0; HCF = 14.
Question bank
Tap to reveal →
A factory produces items in batches of 24 and 36. What is the smallest number of items that can be produced to have complete batches of both types?
A · 72
LCM of 24 and 36 is 72; smallest number for complete batches of both.
Question bank
Tap to reveal →
Which of the following is NOT a factor of 60?
C · 7
7 does not divide 60 exactly, so it is not a factor.
Question bank
Tap to reveal →
If a number is divisible by both 4 and 6, which of the following must it be divisible by?
B · 12
LCM of 4 and 6 is 12; number divisible by both must be divisible by 12.
Question bank
Tap to reveal →
Two buses start from the same point at the same time. One bus completes a round in 40 minutes, the other in 50 minutes. After how many minutes will they meet again at the starting point?
A · 200
LCM of 40 and 50 is 200 minutes; they meet again after 200 minutes.
Question bank
Tap to reveal →
A man takes 12 minutes to walk around a park, and a woman takes 15 minutes. If they start together, after how many minutes will they meet again at the starting point?
B · 60
LCM of 12 and 15 is 60 minutes; they meet again after 60 minutes.
Question bank
Tap to reveal →
Three bells ring at intervals of 12, 15, and 20 minutes respectively. If they ring together at 8:00 AM, when will they ring together next?
D · 9:00 AM
LCM of 12, 15, and 20 is 60 minutes; next ringing together at 9:00 AM.
Question bank
Tap to reveal →
A clock chimes every 15 minutes and a bell rings every 20 minutes. If both chime together at 6:00 PM, when will they next chime together?
B · 7:00 PM
LCM of 15 and 20 is 60 minutes; next together at 7:00 PM.
Question bank
Tap to reveal →
Let positive integers x and y satisfy the conditions: HCF(x,y) = 21, LCM(x,y) = 1764, and x + y = 189. If x and y are both multiples of a prime p > 7, find p.
B · 13
Question bank
Tap to reveal →
Three numbers a, b, c satisfy: HCF(a,b) = 12, HCF(b,c) = 18, HCF(a,c) = 24, and LCM(a,b,c) = 4320. If a, b, c are pairwise coprime after dividing by their respective HCFs, find the value of a + b + c.
C · 204
Question bank
Tap to reveal →
If two numbers A and B satisfy that their HCF is 84 and their LCM is 9240, and the sum of A and B is 546, find the difference between A and B.
A · 210
Question bank
Tap to reveal →
Assertion (A): If the LCM of two numbers is equal to the product of the numbers, then their HCF is 1.
Reason (R): The product of two numbers is always greater than or equal to their LCM multiplied by their HCF.
A · Both A and R are true and R is the correct explanation of A
Question bank
Tap to reveal →
Two numbers are such that their HCF is 15 and their LCM is 1800. If one of the numbers is 75, find the other number and verify if it is a multiple of 45.
A · 360, Yes
Question bank
Tap to reveal →
If the HCF of two numbers is 35 and their difference is 105, which of the following can be their LCM?
B · 1575
Question bank
Tap to reveal →
If the LCM of two numbers is 4620 and their HCF is 21, and the difference between the numbers is 84, find the sum of the two numbers.
A · 693
Question bank
Tap to reveal →
Assertion (A): For any two positive integers, the product of their HCF and LCM is equal to the product of the numbers.
Reason (R): The prime factorization of the numbers determines their HCF and LCM uniquely.
A · Both A and R are true and R is the correct explanation of A
Question bank
Tap to reveal →
If the HCF of three numbers is 6 and their LCM is 2160, and the numbers are in the ratio 3:5:8, find the numbers.
C · 54, 90, 144
Question bank
Tap to reveal →
The LCM of two numbers is 2520 and their HCF is 14. If one number is 126, find the other number and check if it is a multiple of 18.
A · 280, No
Question bank
Tap to reveal →
Assertion (A): The LCM of two numbers is always greater than or equal to their maximum.
Reason (R): The LCM is the smallest number divisible by both numbers.
A · Both A and R are true and R is the correct explanation of A
Question bank
Tap to reveal →
If the HCF of two numbers is 12 and their LCM is 180, and the sum of the numbers is 84, find the numbers.
A · 24 and 60
Question bank
Tap to reveal →
Match the following HCF-LCM pairs with possible pairs of numbers:
Column A:
1) HCF=4, LCM=180
2) HCF=6, LCM=360
3) HCF=8, LCM=224
4) HCF=10, LCM=450
Column B:
A) (12, 60)
B) (18, 120)
C) (16, 112)
D) (30, 150)
A · 1-A, 2-B, 3-C, 4-D
Question bank
Tap to reveal →
If the HCF of two numbers is 9 and their product is 7290, which of the following can be their LCM?
A · 810
Step 1: Let numbers be 9x and 9y with gcd(x,y)=1.
Step 2: Product = 9x * 9y = 81xy = 7290 => xy = 7290 / 81 = 90.
Step 3: LCM = 9 * x * y = 9 * 90 = 810.
Step 4: So LCM is 810.
Question bank
Tap to reveal →
Two numbers have HCF 18 and LCM 1260. If one number is 90, find the other number and check if it is divisible by 14.
A · 252, Yes
Step 1: Let other number be x.
Step 2: Product = HCF * LCM = 18 * 1260 = 22680.
Step 3: 90 * x = 22680 => x = 22680 / 90 = 252.
Step 4: Check divisibility by 14: 14*18=252, so yes.
Question bank
Tap to reveal →
Assertion (A): If the HCF of two numbers is 1, then their LCM is always equal to their product.
Reason (R): Two numbers are coprime if their HCF is 1.
A · Both A and R are true and R is the correct explanation of A
