Quick recall · 248 cards
Short MCQ-style retrieval prompts. Tap a card to reveal the answer.
PYQ
Tap to reveal →
Which of the following is a prime number?
C · 571
PYQ
Tap to reveal →
What is the smallest positive integer that is divisible by both \( 11^2 \) and \( 3^3 \), and when multiplied by a certain integer 'a' gives the number 55440?
C · 24
PYQ
Tap to reveal →
If a : b = 5 : 3, what percentage of 3a is (3a + 4b)?
D · (D) 180%
PYQ
Tap to reveal →
A and B together have Rs. 1210. If \( \frac{15}{16} \) of A's amount is equal to \( \frac{4}{5} \) of B's amount, how much amount does B have?
A · Rs. 1210
PYQ
Tap to reveal →
Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
C · 7:8:9
PYQ
Tap to reveal →
The average age of a group of 12 students is 20 years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is ____
A · 24
PYQ
Tap to reveal →
Find the mean of the following numbers: 10, 39, 71, 39, 76, 38, 25
C · c. 40
PYQ
Tap to reveal →
Find the median of the following data: 1, 6, 12, 19, 5, 0, 6
A · A. 6
Arrange in ascending order: 0, 1, 5, 6, 6, 12, 19n = 7 (odd), median = 4th term = 6Option **A** is correct.
PYQ
Tap to reveal →
Find the median of the data: 5, 7, 4, 9, 5, 4, 4, 3
D · D. 4
Question bank
Tap to reveal →
What is the value of \( 345 + 678 \)?
A · 1023
Adding 345 and 678 gives 1023.
Question bank
Tap to reveal →
Calculate \( 144 \div 12 \).
B · 12
Dividing 144 by 12 gives 12.
Question bank
Tap to reveal →
If \( x = 5 \) and \( y = 3 \), what is the value of \( 2x + 3y \)?
A · 19
Substitute values: \( 2 \times 5 + 3 \times 3 = 10 + 9 = 19 \). Option A is 19, but options are mismatched, correct is 19.
Question bank
Tap to reveal →
Which of the following properties states that \( a + b = b + a \)?
C · Commutative Property
The commutative property states that the order of addition or multiplication does not affect the result.
Question bank
Tap to reveal →
Which property is illustrated by \( (a + b) + c = a + (b + c) \)?
B · Associative Property
The associative property refers to the grouping of numbers in addition or multiplication.
Question bank
Tap to reveal →
Which of the following shows the distributive property?
A · \( a(b + c) = ab + ac \)
The distributive property states that multiplication distributes over addition.
Question bank
Tap to reveal →
Which number is a prime number?
B · 29
29 is a prime number as it has only two factors: 1 and 29.
Question bank
Tap to reveal →
Identify the composite number from the options below.
C · 27
27 is composite because it has factors other than 1 and itself (e.g., 3 and 9).
Question bank
Tap to reveal →
Which of the following is an odd prime number?
C · 7
7 is an odd prime number; 2 is prime but even.
Question bank
Tap to reveal →
Evaluate \( 8 + 2 \times 5 \) using the correct order of operations.
B · 18
According to BODMAS, multiplication before addition: \( 2 \times 5 = 10 \), then \( 8 + 10 = 18 \).
Question bank
Tap to reveal →
Calculate \( (15 - 3) \times (12 \div 4) \).
A · 36
First, calculate inside parentheses: \( 15 - 3 = 12 \), \( 12 \div 4 = 3 \). Then multiply: \( 12 \times 3 = 36 \). Correct answer is 36 (Option A).
Question bank
Tap to reveal →
Evaluate \( 6 + 4 \times (3^2 - 5) \div 2 \) using BODMAS.
A · 14
Calculate inside parentheses: \( 3^2 - 5 = 9 - 5 = 4 \). Then multiplication and division: \( 4 \times 4 = 16 \), \( 16 \div 2 = 8 \). Finally addition: \( 6 + 8 = 14 \).
Question bank
Tap to reveal →
A shopkeeper buys 20 items at Rs 15 each and sells them for Rs 18 each. What is his profit?
A · Rs 60
Cost price = 20 \times 15 = Rs 300. Selling price = 20 \times 18 = Rs 360. Profit = 360 - 300 = Rs 60.
Question bank
Tap to reveal →
If the sum of two numbers is 45 and one number is 27, what is the other number?
A · 18
Other number = 45 - 27 = 18.
Question bank
Tap to reveal →
What is the result of \( 125 + 376 \)?
A · 501
Adding 125 and 376 gives 501.
Question bank
Tap to reveal →
Calculate \( 84 \times 7 \).
A · 588
Multiplying 84 by 7 results in 588.
Question bank
Tap to reveal →
Which of the following shows the correct subtraction of \( 732 - 489 \)?
A · 243
Subtracting 489 from 732 gives 243.
Question bank
Tap to reveal →
Which property of addition is illustrated by \( 5 + (8 + 3) = (5 + 8) + 3 \)?
B · Associative property
The associative property states that grouping of numbers does not affect the sum.
Question bank
Tap to reveal →
Which of the following demonstrates the distributive property?
A · \( 3 \times (4 + 5) = 3 \times 4 + 3 \times 5 \)
Distributive property states multiplication over addition: \( a(b + c) = ab + ac \).
Question bank
Tap to reveal →
If \( (6 + 2) + 5 = 6 + (2 + 5) \), which property is being used?
B · Associative
The associative property allows regrouping without changing the sum.
Question bank
Tap to reveal →
Which of the following is a composite number?
C · 35
35 has factors other than 1 and itself (5 and 7), so it is composite.
Question bank
Tap to reveal →
Identify the number type of \( -12 \).
C · Integer
Negative numbers are integers but not whole or natural numbers.
Question bank
Tap to reveal →
Which of the following numbers is both prime and odd?
C · 11
11 is a prime number and is odd.
Question bank
Tap to reveal →
Evaluate \( 8 + 3 \times 5 - 4 \div 2 \) using the correct order of operations.
A · 21
First multiply and divide: \(3 \times 5 = 15\), \(4 \div 2 = 2\). Then add and subtract: \(8 + 15 - 2 = 21\).
Question bank
Tap to reveal →
Find the value of \( (12 - 3) \times (6 + 2) \div 4 \).
A · 18
Calculate inside parentheses: \(12 - 3 = 9\), \(6 + 2 = 8\). Then multiply and divide: \(9 \times 8 = 72\), \(72 \div 4 = 18\).
Question bank
Tap to reveal →
Evaluate \( 5 + 2 \times (9 - 4)^2 \div 5 \).
B · 15
Question bank
Tap to reveal →
A shopkeeper buys 12 pens at Rs 15 each and sells them all at Rs 20 each. What is his profit?
A · Rs 60
Cost price = 12 \times 15 = Rs 180Selling price = 12 \times 20 = Rs 240Profit = 240 - 180 = Rs 60
Question bank
Tap to reveal →
If \( \frac{3}{4} \) of a number is 48, what is the number?
A · 64
Let the number be \( x \). Then \( \frac{3}{4} x = 48 \) implies \( x = \frac{48 \times 4}{3} = 64 \).
Question bank
Tap to reveal →
Which of the following sets contains only natural numbers?
A · {1, 2, 3, 4}
Natural numbers are positive integers starting from 1, so {1, 2, 3, 4} contains only natural numbers.
Question bank
Tap to reveal →
Which of the following numbers is a whole number?
B · 0
Whole numbers include all natural numbers and zero, so 0 is a whole number.
Question bank
Tap to reveal →
Which of the following is an irrational number?
C · \( \sqrt{3} \)
\( \sqrt{3} \) is an irrational number because it cannot be expressed as a ratio of two integers.
Question bank
Tap to reveal →
Which of the following numbers is both rational and an integer?
B · -4
-4 is an integer and can be expressed as \( \frac{-4}{1} \), so it is rational.
Question bank
Tap to reveal →
Identify the set to which the number \( -\frac{7}{3} \) belongs.
C · Rational numbers
\( -\frac{7}{3} \) is a ratio of two integers and hence a rational number.
Question bank
Tap to reveal →
Which of the following numbers is a prime number?
B · 29
29 is a prime number as it has only two factors: 1 and 29.
Question bank
Tap to reveal →
Which of the following is a composite number?
C · 39
39 is composite because it has factors other than 1 and itself (3 and 13).
Question bank
Tap to reveal →
Find the smallest prime number greater than 50.
B · 53
53 is prime; 51, 55, and 57 are composite.
Question bank
Tap to reveal →
Which of the following numbers is prime?
B · 97
97 is a prime number; 91, 99, and 100 are composite.
Question bank
Tap to reveal →
How many prime numbers are there between 30 and 50?
C · 4
The prime numbers between 30 and 50 are 31, 37, 41, and 43 (4 in total).
Question bank
Tap to reveal →
Which of the following numbers is divisible by 4?
A · 124
124 ends with '24' which is divisible by 4, so 124 is divisible by 4.
Question bank
Tap to reveal →
Which number is divisible by both 3 and 9?
D · 216
216 is divisible by 9 (sum of digits 2+1+6=9) and hence divisible by 3 as well.
Question bank
Tap to reveal →
Which of the following numbers is divisible by 11?
A · 121
121 is divisible by 11 (11 \times 11 = 121).
Question bank
Tap to reveal →
Find the smallest number divisible by 2, 3, and 5.
C · 30
LCM of 2, 3, and 5 is 30, which is the smallest number divisible by all three.
Question bank
Tap to reveal →
Which of the following numbers is divisible by 6 but not by 9?
C · 84
84 is divisible by 6 (2 and 3) but sum of digits (8+4=12) is not divisible by 9.
Question bank
Tap to reveal →
Find the highest common factor (HCF) of 36 and 48.
B · 12
HCF of 36 and 48 is 12.
Question bank
Tap to reveal →
What is the least common multiple (LCM) of 8 and 12?
A · 24
LCM of 8 and 12 is 24.
Question bank
Tap to reveal →
Find the HCF of 56, 98, and 112.
B · 14
HCF of 56, 98, and 112 is 14.
Question bank
Tap to reveal →
Find the LCM of 15, 20, and 30.
A · 60
LCM of 15, 20, and 30 is 60.
Question bank
Tap to reveal →
If the HCF of two numbers is 12 and their LCM is 180, what is the product of the two numbers?
B · 2160
Product of two numbers = HCF \( \times \) LCM = 12 \( \times \) 180 = 2160.
Question bank
Tap to reveal →
Which of the following numbers is odd?
C · 4097
4097 ends with 7, which is an odd digit, so the number is odd.
Question bank
Tap to reveal →
Which of the following sums is odd?
C · Even + Odd
Sum of an even and an odd number is always odd.
Question bank
Tap to reveal →
What is the parity of the product of two odd numbers?
B · Odd
Product of two odd numbers is always odd.
Question bank
Tap to reveal →
If the sum of two numbers is odd, then one number is even and the other is:
B · Odd
Sum of an even and an odd number is odd.
Question bank
Tap to reveal →
Which of the following is true about zero?
B · Zero is an even number
Zero is an even number because it is divisible by 2.
Question bank
Tap to reveal →
Which of the following statements is correct about the number one?
C · One is neither prime nor composite
One is neither prime nor composite by definition.
Question bank
Tap to reveal →
Which of the following is true for any negative number \( x \)?
B · \( x^2 \) is positive
Square of any negative number is positive.
Question bank
Tap to reveal →
If \( a \) is a negative number, which of the following is true?
A · \( a + |a| = 0 \)
Since \( |a| = -a \) for negative \( a \), \( a + |a| = a - a = 0 \).
Question bank
Tap to reveal →
If the sum of digits of a number is divisible by 9, then the number is divisible by:
C · Both 3 and 9
If sum of digits is divisible by 9, the number is divisible by both 3 and 9.
Question bank
Tap to reveal →
Which of the following numbers is divisible by 11?
A · 2728
Difference between sum of digits in odd and even positions for 2728 is (2+2) - (7+8) = 4 - 15 = -11, divisible by 11.
Question bank
Tap to reveal →
Find the sum of digits of the number 12345 and determine if it is divisible by 3.
A · Sum = 15, divisible by 3
Sum of digits = 1+2+3+4+5 = 15, which is divisible by 3.
Question bank
Tap to reveal →
Which of the following numbers is a perfect number?
A · 6
6 is a perfect number because the sum of its proper divisors (1, 2, 3) equals 6.
Question bank
Tap to reveal →
Which of the following pairs are amicable numbers?
D · All of the above
All listed pairs are amicable numbers where each number is the sum of the proper divisors of the other.
Question bank
Tap to reveal →
Which of the following numbers is NOT a perfect square?
D · 180
180 is not a perfect square; others are squares of 12, 13, and 14 respectively.
Question bank
Tap to reveal →
If the first term of an arithmetic progression is 3 and the common difference is 5, what is the 10th term?
A · 48
The 10th term \( a_{10} = a_1 + 9d = 3 + 9 \times 5 = 3 + 45 = 48 \). Correction: 48 is correct, so option A is correct.
Question bank
Tap to reveal →
What is the sum of the first 15 terms of the arithmetic progression: 2, 5, 8, ...?
A · 345
Sum \( S_n = \frac{n}{2} [2a + (n-1)d] = \frac{15}{2} [2 \times 2 + 14 \times 3] = \frac{15}{2} [4 + 42] = \frac{15}{2} \times 46 = 345 \).
Question bank
Tap to reveal →
In an arithmetic progression, the 5th term is 20 and the 10th term is 35. What is the first term?
B · 8
Let first term be \( a \) and common difference \( d \). \( a + 4d = 20 \), \( a + 9d = 35 \). Subtracting: \( 5d = 15 \) so \( d = 3 \). Then \( a = 20 - 4 \times 3 = 8 \).
Question bank
Tap to reveal →
Find the 12th term of the arithmetic progression where the first term is 7 and the sum of the first 12 terms is 234.
C · 26
Question bank
Tap to reveal →
Which of the following numbers is divisible by 11?
C · 286
Question bank
Tap to reveal →
Which of the following numbers is divisible by 9?
D · 567
A number is divisible by 9 if the sum of its digits is divisible by 9. For 567, sum of digits = 5 + 6 + 7 = 18, which is divisible by 9.
Question bank
Tap to reveal →
Find the smallest positive integer divisible by both 4 and 6 but not by 8.
A · 12
LCM of 4 and 6 is 12. 12 is divisible by 4 and 6 but not by 8.
Question bank
Tap to reveal →
Which of the following numbers is NOT divisible by 7?
D · 378
Question bank
Tap to reveal →
Which of the following numbers is divisible by 13?
A · 169
169 = 13 × 13, so it is divisible by 13.
Question bank
Tap to reveal →
Find the remainder when 2^{10} is divided by 11.
A · 1
By Fermat's Little Theorem, 2^{10} mod 11 = 1.
Question bank
Tap to reveal →
Which of the following is a prime number?
B · 53
53 is a prime number; others are composite.
Question bank
Tap to reveal →
Which of the following numbers is composite?
C · 35
35 = 5 × 7, so it is composite.
Question bank
Tap to reveal →
Which of the following numbers is a twin prime with 41?
B · 43
Twin primes are pairs of primes differing by 2. 41 and 43 form a twin prime pair.
Question bank
Tap to reveal →
Which of the following is the smallest prime factor of 221?
B · 13
221 = 13 × 17, but 13 is the smallest prime factor, so correct answer is B. Correction: 221 ÷ 13 = 17, so smallest prime factor is 13.
Question bank
Tap to reveal →
Which of the following numbers is a prime number greater than 50?
B · 53
53 is prime; others are composite.
Question bank
Tap to reveal →
How many factors does the number 36 have?
B · 9
36 = 2^2 × 3^2; number of factors = (2+1)(2+1) = 9.
Question bank
Tap to reveal →
Which of the following is the least common multiple (LCM) of 8 and 12?
A · 24
LCM of 8 and 12 is 24.
Question bank
Tap to reveal →
Find the greatest common divisor (GCD) of 54 and 72.
C · 18
GCD of 54 and 72 is 18.
Question bank
Tap to reveal →
Which of the following numbers is a multiple of both 7 and 9?
B · 63
63 is divisible by both 7 and 9.
Question bank
Tap to reveal →
Find the number of positive factors of 360.
B · 24
360 = 2^3 × 3^2 × 5^1; number of factors = (3+1)(2+1)(1+1) = 4×3×2=24.
Question bank
Tap to reveal →
Find the GCD of 84, 126, and 210.
C · 42
Prime factorization: 84 = 2^2 × 3 × 7, 126 = 2 × 3^2 × 7, 210 = 2 × 3 × 5 × 7. Common factors: 2 × 3 × 7 = 42.
Question bank
Tap to reveal →
What is the LCM of 15, 20, and 30?
A · 60
LCM is the smallest number divisible by all: 60.
Question bank
Tap to reveal →
If \( \text{GCD}(x, 24) = 6 \) and \( \text{LCM}(x, 24) = 72 \), find \( x \).
B · 18
Using \( x \times 24 = \text{GCD} \times \text{LCM} \), so \( x = \frac{6 \times 72}{24} = 18 \).
Question bank
Tap to reveal →
Find the LCM of 8 and 14.
A · 56
LCM of 8 and 14 is 56.
Question bank
Tap to reveal →
Find the GCD of 96 and 180.
B · 24
GCD of 96 and 180 is 24.
Question bank
Tap to reveal →
Find the GCD of 210, 462, and 770.
Question bank
Tap to reveal →
Find the LCM of 9, 12, and 15.
Question bank
Tap to reveal →
Which of the following is an odd number?
B · 357
357 ends with 7, which is odd.
Question bank
Tap to reveal →
Sum of two even numbers is always:
A · Even
Sum of two even numbers is always even.
Question bank
Tap to reveal →
If \( n \) is an odd integer, which of the following is always even?
A · \( n + 1 \)
Adding 1 to an odd number results in an even number.
Question bank
Tap to reveal →
If \( a \) and \( b \) are odd integers, what is the parity of \( a \times b \)?
B · Odd
Product of two odd numbers is always odd.
Question bank
Tap to reveal →
Convert decimal number 156 to base 8.
B · 244
156 in base 8 is 244.
Question bank
Tap to reveal →
What is the decimal equivalent of binary number 11011?
A · 27
\( 1\times2^4 + 1\times2^3 + 0\times2^2 + 1\times2^1 + 1\times2^0 = 16 + 8 + 0 + 2 + 1 = 27 \). Correction: Sum is 27, so correct answer is A.
Question bank
Tap to reveal →
Convert hexadecimal number A3 to decimal.
A · 163
A = 10, so \( 10 \times 16 + 3 = 163 \).
Question bank
Tap to reveal →
What is the binary equivalent of decimal number 45?
A · 101101
45 in binary is 101101.
Question bank
Tap to reveal →
What is the decimal value of base-5 number 243?
B · 73
2×25 + 4×5 + 3 = 50 + 20 + 3 = 73.
Question bank
Tap to reveal →
Which of the following integers is negative?
Question bank
Tap to reveal →
What is the absolute value of \(-27\)?
C · 27
Absolute value of -27 is 27.
Question bank
Tap to reveal →
If \( a = -5 \) and \( b = 3 \), what is \( a - b \)?
Question bank
Tap to reveal →
Which of the following numbers is a perfect square?
B · 64
64 = 8^2 is a perfect square.
Question bank
Tap to reveal →
Which of the following is a perfect cube?
A · 27
27 = 3^3 is a perfect cube.
Question bank
Tap to reveal →
Which of the following numbers is a perfect number?
A · 6
6 is a perfect number because sum of its divisors (1+2+3) equals 6.
Question bank
Tap to reveal →
Which of the following pairs are amicable numbers?
D · (All of the above)
All given pairs are amicable numbers.
Question bank
Tap to reveal →
What is the remainder when 12345 is divided by 9?
C · 6
Sum of digits = 1+2+3+4+5=15; remainder when 15 is divided by 9 is 6. Correction: 15 mod 9 = 6, so remainder is 6.
Question bank
Tap to reveal →
Find the remainder when \( 7^{100} \) is divided by 5.
B · 1
Since 7 mod 5 = 2, \( 7^{100} \equiv 2^{100} \) mod 5. Powers of 2 mod 5 cycle every 4: 2^4=16 mod 5=1. 100 mod 4=0, so remainder is 1.
Question bank
Tap to reveal →
If \( a \equiv 3 \pmod{7} \) and \( b \equiv 5 \pmod{7} \), find \( (a+b) \pmod{7} \).
A · 1
\( (3 + 5) \mod 7 = 8 \mod 7 = 1 \).
Question bank
Tap to reveal →
What is the digital root of 9876?
B · 3
Sum digits: 9+8+7+6=30; sum digits of 30=3+0=3.
Question bank
Tap to reveal →
Which of the following numbers has a digital root of 9?
B · 999
999 sum digits = 27, sum digits again = 9.
Question bank
Tap to reveal →
If the sum of digits of a number is divisible by 3, then the number is divisible by:
A · 3
Divisibility by 3 depends on sum of digits being divisible by 3.
Question bank
Tap to reveal →
Using casting out nines, find the remainder when 4567 is divided by 9.
D · 4
Sum digits = 4+5+6+7=22; 22 mod 9 = 4; remainder is 4.
Question bank
Tap to reveal →
Let \(N\) be the smallest positive integer such that \(N\) is divisible by 84, the sum of its digits is 24, and \(N\) leaves a remainder of 7 when divided by 13. What is the value of \(N\)?
D · 672
Question bank
Tap to reveal →
Consider the set \(S = \{x \in \mathbb{N} : x < 10^5, x \equiv 3 \pmod{7}, x \equiv 5 \pmod{11}, \text{and } x \text{ is divisible by } 13\}. Find the sum of all elements in \(S\).
C · 1,470,000
Question bank
Tap to reveal →
If \(a\) and \(b\) are two positive integers such that \(\gcd(a,b) = 21\), \(\mathrm{lcm}(a,b) = 8820\), and the difference \(|a-b|\) is a multiple of 35, find the number of possible ordered pairs \((a,b)\).
B · 6
Question bank
Tap to reveal →
Find the number of positive integers \(n < 10^6\) such that \(n\) is divisible by 18, the sum of digits of \(n\) is divisible by 9, and \(n^2\) ends with the digits 376.
B · 1
Question bank
Tap to reveal →
Let \(p\) be a prime number greater than 5. Consider the number \(N = p^4 - p^2 + 1\). Which of the following statements is always true?
C · \(N\) is divisible by 13
Question bank
Tap to reveal →
Let \(x\) be the smallest positive integer such that \(x \equiv 2 \pmod{5}\), \(x \equiv 3 \pmod{7}\), and \(x \equiv 4 \pmod{9}\). Find the value of \(x^2 \pmod{315}\).
B · 169
Question bank
Tap to reveal →
Let \(n\) be a positive integer such that \(n^2 + n + 1\) is divisible by 7. Find the number of such \(n\) with \(1 \leq n \leq 1000\).
B · 143
Question bank
Tap to reveal →
Find the smallest positive integer \(k\) such that \(7^k \equiv 1 \pmod{100}\).
A · 20
Question bank
Tap to reveal →
If \(a\) and \(b\) are positive integers such that \(a^2 + b^2\) is divisible by 13, which of the following must be true?
D · \(a \equiv \pm 2b \pmod{13}\)
Question bank
Tap to reveal →
Which of the following represents the fraction \( \frac{3}{4} \) in decimal form?
B · 0.75
Dividing 3 by 4 gives 0.75, so \( \frac{3}{4} = 0.75 \).
Question bank
Tap to reveal →
What is the numerator in the fraction \( \frac{7}{9} \)?
A · 7
The numerator is the number above the fraction line, which is 7.
Question bank
Tap to reveal →
Which of the following fractions is equivalent to \( \frac{2}{5} \)?
A · \( \frac{4}{10} \)
Multiplying numerator and denominator of \( \frac{2}{5} \) by 2 gives \( \frac{4}{10} \), which is equivalent.
Question bank
Tap to reveal →
If \( \frac{5}{8} \) is converted to a decimal, what is the result?
A · 0.625
Dividing 5 by 8 gives 0.625.
Question bank
Tap to reveal →
Calculate \( \frac{3}{7} + \frac{2}{7} \).
B · \( \frac{5}{7} \)
Since denominators are the same, add numerators: 3 + 2 = 5, so \( \frac{5}{7} \).
Question bank
Tap to reveal →
Find the result of \( \frac{7}{12} - \frac{1}{4} \).
C · \( \frac{1}{3} \)
Question bank
Tap to reveal →
Multiply \( \frac{3}{5} \) by \( \frac{10}{9} \).
A · \( \frac{2}{3} \)
Multiply numerators and denominators: \( \frac{3 \times 10}{5 \times 9} = \frac{30}{45} = \frac{2}{3} \).
Question bank
Tap to reveal →
Divide \( \frac{4}{7} \) by \( \frac{2}{3} \).
A · \( \frac{6}{7} \)
Dividing by a fraction is multiplying by its reciprocal: \( \frac{4}{7} \times \frac{3}{2} = \frac{12}{14} = \frac{6}{7} \).
Question bank
Tap to reveal →
Calculate \( \frac{5}{6} + \frac{7}{8} \).
A · \( \frac{59}{48} \)
Question bank
Tap to reveal →
Convert the decimal 0.625 to a fraction in simplest form.
A · \( \frac{5}{8} \)
0.625 = \( \frac{625}{1000} \). Simplify by dividing numerator and denominator by 125: \( \frac{5}{8} \).
Question bank
Tap to reveal →
Which decimal is equivalent to \( \frac{7}{20} \)?
A · 0.35
Dividing 7 by 20 gives 0.35.
Question bank
Tap to reveal →
Convert \( 0.875 \) to a fraction in simplest form.
A · \( \frac{7}{8} \)
0.875 = \( \frac{875}{1000} \) = \( \frac{7}{8} \) after simplification.
Question bank
Tap to reveal →
Express \( \frac{9}{40} \) as a decimal.
A · 0.225
Dividing 9 by 40 gives 0.225.
Question bank
Tap to reveal →
What is the place value of 7 in the decimal number 45.376?
D · 7 thousandths
In 45.376, the digit 7 is in the thousandths place.
Question bank
Tap to reveal →
In the decimal 0.508, which digit is in the hundredths place?
B · 0
The hundredths place is the second digit after the decimal point, which is 0.
Question bank
Tap to reveal →
What is the value of the digit 3 in the number 12.034?
D · 3 thousandths
3 is in the thousandths place, so its value is 3 thousandths.
Question bank
Tap to reveal →
In the decimal number 0.462, what digit is in the tenths place?
A · 4
The tenths place is the first digit after the decimal point, which is 4.
Question bank
Tap to reveal →
Calculate \( 3.75 + 4.2 \).
A · 7.95
Adding decimals: 3.75 + 4.2 = 7.95.
Question bank
Tap to reveal →
Subtract 5.6 from 9.3.
Question bank
Tap to reveal →
Multiply 0.4 by 0.3.
A · 0.12
0.4 × 0.3 = 0.12.
Question bank
Tap to reveal →
Divide 6.4 by 0.8.
Question bank
Tap to reveal →
What is the product of 1.25 and 0.4?
Question bank
Tap to reveal →
Which is greater: \( \frac{3}{5} \) or 0.6?
C · Both are equal
\( \frac{3}{5} = 0.6 \), so both are equal.
Question bank
Tap to reveal →
Arrange the following in ascending order: 0.45, \( \frac{2}{5} \), 0.5, \( \frac{9}{20} \).
D · \( \frac{9}{20} \), 0.45, \( \frac{2}{5} \), 0.5
Question bank
Tap to reveal →
Which fraction is the smallest among \( \frac{5}{8} \), 0.7, \( \frac{3}{4} \), and 0.65?
A · \( \frac{5}{8} \)
\( \frac{5}{8} = 0.625 \), which is less than 0.65, 0.7, and \( \frac{3}{4} = 0.75 \).
Question bank
Tap to reveal →
Arrange the numbers \( \frac{7}{10} \), 0.72, \( \frac{3}{4} \), and 0.68 in descending order.
C · \( \frac{3}{4} \), 0.72, \( \frac{7}{10} \), 0.68
Convert fractions to decimals: \( \frac{7}{10} = 0.7 \), \( \frac{3}{4} = 0.75 \). Descending order: 0.75, 0.72, 0.7, 0.68.
Question bank
Tap to reveal →
Simplify the fraction \( \frac{36}{48} \).
A · \( \frac{3}{4} \)
GCD of 36 and 48 is 12. Dividing numerator and denominator by 12 gives \( \frac{3}{4} \).
Question bank
Tap to reveal →
Reduce \( \frac{45}{60} \) to its simplest form.
A · \( \frac{3}{4} \)
GCD of 45 and 60 is 15. Dividing numerator and denominator by 15 gives \( \frac{3}{4} \).
Question bank
Tap to reveal →
Simplify \( \frac{56}{98} \).
A · \( \frac{4}{7} \)
GCD of 56 and 98 is 14. Dividing numerator and denominator by 14 gives \( \frac{4}{7} \).
Question bank
Tap to reveal →
Reduce \( \frac{81}{108} \) to simplest form.
A · \( \frac{3}{4} \)
GCD of 81 and 108 is 27. Dividing numerator and denominator by 27 gives \( \frac{3}{4} \).
Question bank
Tap to reveal →
A recipe requires \( \frac{3}{4} \) cup of sugar. If you want to make half the recipe, how much sugar is needed?
A · \( \frac{3}{8} \) cup
Half of \( \frac{3}{4} \) is \( \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} \).
Question bank
Tap to reveal →
If a car travels 0.6 of a kilometer in one minute, how far will it travel in 15 minutes?
A · 9 km
Distance = speed × time = 0.6 × 15 = 9 km.
Question bank
Tap to reveal →
A tank is \( \frac{5}{8} \) full of water. If \( \frac{1}{4} \) of the water is used, what fraction of the tank remains full?
B · \( \frac{5}{8} \times \frac{3}{4} \)
Water remaining = \( \frac{5}{8} \times \left(1 - \frac{1}{4}\right) = \frac{5}{8} \times \frac{3}{4} = \frac{15}{32} \).
Question bank
Tap to reveal →
A shopkeeper sold \( \frac{3}{5} \) of his stock and had 120 items left. What was the total number of items initially?
B · 300
If \( \frac{3}{5} \) sold, \( \frac{2}{5} \) remains. \( \frac{2}{5} \) of total = 120, so total = \( 120 \times \frac{5}{2} = 300 \). Option B is 300, so correct answer is B.
Question bank
Tap to reveal →
A student scored 72.5% in an exam. Express this score as a decimal.
A · 0.725
Percent to decimal: divide by 100, so 72.5% = 0.725.
Question bank
Tap to reveal →
If \( \frac{2}{3} \) of a number is 48, what is the number?
A · 72
Let number be x. \( \frac{2}{3} x = 48 \) implies \( x = 48 \times \frac{3}{2} = 72 \).
Question bank
Tap to reveal →
A tank is filled to \( \frac{7}{10} \) of its capacity. After removing 84 liters, it is \( \frac{1}{2} \) full. What is the capacity of the tank?
B · 280 liters
Question bank
Tap to reveal →
Which of the following represents the fraction \( \frac{3}{5} \) in decimal form?
B · 0.6
Dividing 3 by 5 gives 0.6, which is the decimal equivalent of \( \frac{3}{5} \).
Question bank
Tap to reveal →
What is the sum of \( \frac{2}{7} \) and \( \frac{3}{14} \)?
B · \( \frac{7}{14} \)
Options are incorrect or repeated; correct sum is \( \frac{2}{7} + \frac{3}{14} = \frac{4}{14} + \frac{3}{14} = \frac{7}{14} = \frac{1}{2} \).
Question bank
Tap to reveal →
Which of the following fractions is equivalent to \( \frac{12}{18} \)?
A · \( \frac{2}{3} \)
Simplifying \( \frac{12}{18} \) by dividing numerator and denominator by 6 gives \( \frac{2}{3} \).
Question bank
Tap to reveal →
Identify the fraction represented by the decimal 0.125.
A · \( \frac{1}{8} \)
0.125 equals \( \frac{125}{1000} \), which simplifies to \( \frac{1}{8} \).
Question bank
Tap to reveal →
Calculate \( \frac{5}{8} \times \frac{16}{25} \).
B · \( \frac{2}{5} \)
Multiply numerators: 5 \( \times \) 16 = 80; denominators: 8 \( \times \) 25 = 200; \( \frac{80}{200} = \frac{2}{5} \).
Question bank
Tap to reveal →
Which decimal is greater: 0.375 or \( \frac{3}{8} \)?
C · Both are equal
\( \frac{3}{8} = 0.375 \), so both are equal.
Question bank
Tap to reveal →
Simplify the fraction \( \frac{45}{60} \).
A · \( \frac{3}{4} \)
GCD of 45 and 60 is 15; dividing numerator and denominator by 15 gives \( \frac{3}{4} \).
Question bank
Tap to reveal →
Convert the decimal 0.875 to a fraction in simplest form.
A · \( \frac{7}{8} \)
0.875 = \( \frac{875}{1000} \), which simplifies to \( \frac{7}{8} \).
Question bank
Tap to reveal →
What is \( 0.4 + 0.35 \)?
A · 0.75
Adding decimals: 0.4 + 0.35 = 0.75.
Question bank
Tap to reveal →
Subtract \( 0.625 \) from \( 1.25 \).
A · 0.625
1.25 - 0.625 = 0.625.
Question bank
Tap to reveal →
Divide 0.84 by 0.7.
Question bank
Tap to reveal →
Multiply 0.25 by 0.4.
Question bank
Tap to reveal →
Which is the smallest among \( \frac{5}{6} \), 0.83, \( \frac{7}{8} \), and 0.875?
B · 0.83
\( \frac{5}{6} = 0.8333... \), \( \frac{7}{8} = 0.875 \). 0.83 is smallest.
Question bank
Tap to reveal →
Arrange the following in ascending order: 0.5, \( \frac{3}{7} \), 0.45, \( \frac{2}{3} \).
A · 0.45, \( \frac{3}{7} \), 0.5, \( \frac{2}{3} \)
\( \frac{3}{7} \approx 0.4286 \), so order is 0.45, \( \frac{3}{7} \), 0.5, \( \frac{2}{3} = 0.666... \).
Question bank
Tap to reveal →
Which of the following fractions is in simplest form?
C · \( \frac{11}{13} \)
\( \frac{11}{13} \) cannot be simplified further as 11 and 13 are co-prime.
Question bank
Tap to reveal →
Find the equivalent fraction of \( \frac{7}{9} \) with denominator 27.
A · \( \frac{21}{27} \)
Multiply numerator and denominator by 3: \( \frac{7 \times 3}{9 \times 3} = \frac{21}{27} \).
Question bank
Tap to reveal →
A shopkeeper gives a discount of 12.5% on an item priced at Rs. 400. What is the discount amount?
A · Rs. 50
12.5% of 400 = \( \frac{12.5}{100} \times 400 = 50 \). Correction: 12.5% of 400 is Rs. 50, so correct answer is A.
Question bank
Tap to reveal →
If \( \frac{2}{5} \) of a number is 24, what is the number?
A · 60
Let the number be x. \( \frac{2}{5} x = 24 \) \( \Rightarrow x = \frac{24 \times 5}{2} = 60 \).
Question bank
Tap to reveal →
A tank is \( \frac{3}{4} \) full. If 60 liters of water is added, it becomes full. What is the capacity of the tank?
A · 240 liters
Let capacity be x. \( x - \frac{3}{4}x = 60 \) \( \Rightarrow \frac{1}{4}x = 60 \) \( \Rightarrow x = 240 \).
Question bank
Tap to reveal →
Convert 0.333... (recurring) to a fraction.
A · \( \frac{1}{3} \)
0.333... recurring equals \( \frac{1}{3} \).
Question bank
Tap to reveal →
Which decimal is terminating?
A · 0.625
0.625 terminates after three decimal places; others are recurring decimals.
Question bank
Tap to reveal →
Express \( \frac{7}{12} \) as a decimal up to 3 decimal places.
A · 0.583
\( \frac{7}{12} = 0.5833... \), rounded to 3 decimal places is 0.583.
Question bank
Tap to reveal →
Which of the following decimals is recurring?
A · 0.142857
0.142857 is a recurring decimal representing \( \frac{1}{7} \).
Question bank
Tap to reveal →
If \( \frac{4}{x} = 0.8 \), what is the value of \( x \)?
A · 5
\( \frac{4}{x} = 0.8 \) implies \( x = \frac{4}{0.8} = 5 \).
Question bank
Tap to reveal →
What is \( \frac{7}{10} - \frac{2}{5} \)?
A · \( \frac{3}{10} \)
\( \frac{7}{10} - \frac{2}{5} = \frac{7}{10} - \frac{4}{10} = \frac{3}{10} \).
Question bank
Tap to reveal →
Which of the following is the product of \( \frac{3}{4} \) and \( \frac{8}{9} \)?
A · \( \frac{2}{3} \)
Multiply numerators: 3 \( \times \) 8 = 24; denominators: 4 \( \times \) 9 = 36; \( \frac{24}{36} = \frac{2}{3} \).
Question bank
Tap to reveal →
Which decimal is equivalent to \( \frac{9}{20} \)?
A · 0.45
\( \frac{9}{20} = 0.45 \).
Question bank
Tap to reveal →
If \( 0.6 \times x = 1.2 \), find \( x \).
A · 2
\( x = \frac{1.2}{0.6} = 2 \).
Question bank
Tap to reveal →
Which of the following decimals is greater than \( \frac{3}{5} \)?
B · 0.6
\( \frac{3}{5} = 0.6 \). So decimals greater than 0.6 are greater; 0.6 equals \( \frac{3}{5} \).
Question bank
Tap to reveal →
A student scored \( \frac{7}{10} \) of the total marks. If the total marks are 150, what is the student's score?
A · 105
Score = \( \frac{7}{10} \times 150 = 105 \).
Question bank
Tap to reveal →
Which of the following fractions has a terminating decimal representation?
A · \( \frac{3}{8} \)
Fractions with denominators having only 2 and 5 as prime factors have terminating decimals. 8 = 2^3, so \( \frac{3}{8} \) terminates.
Question bank
Tap to reveal →
If \( 0.75 = \frac{m}{n} \) where \( m \) and \( n \) are integers with no common factors, what is \( n \)?
A · 4
0.75 = \( \frac{3}{4} \), so denominator \( n = 4 \).
Question bank
Tap to reveal →
Which of the following is the result of dividing \( \frac{5}{6} \) by \( \frac{10}{9} \)?
A · \( \frac{3}{4} \)
Dividing fractions: \( \frac{5}{6} \div \frac{10}{9} = \frac{5}{6} \times \frac{9}{10} = \frac{45}{60} = \frac{3}{4} \).
Question bank
Tap to reveal →
A recipe requires \( \frac{3}{4} \) cup of sugar. If you want to make half the recipe, how much sugar is needed?
A · \( \frac{3}{8} \) cup
Half of \( \frac{3}{4} \) is \( \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} \).
Question bank
Tap to reveal →
If \( \frac{r}{s} \) is a fraction in lowest terms such that its decimal expansion is repeating with period 6, and \( s \) divides \( 999999 \), which of the following must be true?
B · The denominator \( s \) divides 999999 and the fraction cannot be simplified further
Question bank
Tap to reveal →
Let \( \frac{u}{v} \) be a fraction in lowest terms such that its decimal expansion repeats with period 4. If \( v \) divides \( 9999 \), which of the following is false?
B · The decimal expansion terminates after 4 digits
Question bank
Tap to reveal →
If \( \frac{a}{b} \) is a fraction in lowest terms such that its decimal expansion has a repeating block of length 5, which of the following could be the denominator \( b \)?
A · 31
Question bank
Tap to reveal →
A fraction \( \frac{m}{n} \) in lowest terms has denominator \( n = 2^3 \times 5^2 \times 7 \). Which of the following statements about its decimal expansion is correct?
C · The decimal expansion is repeating with period equal to the order of 10 modulo 7
Question bank
Tap to reveal →
If \( \frac{a}{b} \) is a fraction such that \( a + b = 1001 \) and its decimal expansion terminates, which of the following could be the value of \( b \)?
A · 625
Question bank
Tap to reveal →
Which of the following fractions has a decimal expansion that repeats with the shortest possible period?
A · \( \frac{1}{3} \)
Question bank
Tap to reveal →
If a fraction \( \frac{p}{q} \) in lowest terms has a decimal expansion that terminates after 4 digits, which of the following could NOT be \( q \)?
D · 1250
Question bank
Tap to reveal →
Which of the following represents the ratio of 12 to 8 in simplest form?
A · 3:2
The ratio 12:8 can be simplified by dividing both terms by their greatest common divisor, which is 4. Thus, 12 \div 4 = 3 and 8 \div 4 = 2, so the simplified ratio is 3:2.
Question bank
Tap to reveal →
If the ratio of boys to girls in a class is 5:3, what fraction of the class are girls?
A · \( \frac{3}{8} \)
Total parts = 5 + 3 = 8. Girls represent 3 parts out of 8, so the fraction is \( \frac{3}{8} \).
Question bank
Tap to reveal →
Which of the following is NOT a property of ratios?
A · If \( a:b = c:d \), then \( a + b : b = c + d : d \)
The property stated in option A is incorrect. The correct property is if \( a:b = c:d \), then \( a + b : b \) is not necessarily equal to \( c + d : d \).
Question bank
Tap to reveal →
If \( \frac{a}{b} = \frac{c}{d} \), which of the following is true?
A · a : b = c : d
By definition, if \( \frac{a}{b} = \frac{c}{d} \), then the ratios \( a:b \) and \( c:d \) are equal.
Question bank
Tap to reveal →
If \( a:b = c:d \), then which of the following is the correct proportion?
A · \( a \times d = b \times c \)
The fundamental property of proportion states that if \( a:b = c:d \), then \( a \times d = b \times c \).
Question bank
Tap to reveal →
Which of the following ratios is equivalent to \( 15:25 \)?
A · 3:5
Simplify \( 15:25 \) by dividing both terms by 5: \( 15 \div 5 = 3 \), \( 25 \div 5 = 5 \). So, the equivalent ratio is 3:5.
Question bank
Tap to reveal →
Simplify the ratio \( 48:60 \).
A · 4:5
The greatest common divisor of 48 and 60 is 12. Dividing both by 12 gives \( 48 \div 12 = 4 \) and \( 60 \div 12 = 5 \), so the simplified ratio is 4:5.
Question bank
Tap to reveal →
If the ratio \( x:y = 7:9 \), what is the value of \( 3x + 2y \) in terms of \( y \)?
A · \( \frac{43}{9} y \)
From \( x:y = 7:9 \), \( x = \frac{7}{9} y \). So, \( 3x + 2y = 3 \times \frac{7}{9} y + 2y = \frac{21}{9} y + 2y = \frac{21}{9} y + \frac{18}{9} y = \frac{39}{9} y = \frac{43}{9} y \).
Question bank
Tap to reveal →
Given the continued ratio \( 2:3:5 \), what is the ratio of the first to the third term?
A · 2:5
In a continued ratio \( a:b:c \), the ratio of the first to the third term is simply \( a:c \), which is 2:5 here.
Question bank
Tap to reveal →
If \( a:b = 4:7 \) and \( b:c = 14:15 \), what is the continued ratio \( a:b:c \)?
A · 8:14:15
To combine ratios, make the common term equal. Here, \( b = 7 \) in first ratio and \( b = 14 \) in second. Multiply first ratio by 2: \( 8:14 \). So, continued ratio is \( 8:14:15 \).
Question bank
Tap to reveal →
If \( x:y = 3:4 \) and \( y:z = 8:9 \), find the continued ratio \( x:y:z \).
A · 6:8:9
Make \( y \) common: \( y = 4 \) and \( y = 8 \). Multiply first ratio by 2: \( 6:8 \). So, continued ratio is \( 6:8:9 \).
Question bank
Tap to reveal →
If \( y \) is directly proportional to \( x \) and \( y = 12 \) when \( x = 4 \), what is \( y \) when \( x = 10 \)?
A · 30
Direct proportion means \( y = kx \). When \( x=4, y=12 \), so \( k=3 \). For \( x=10 \), \( y=3 \times 10=30 \).
Question bank
Tap to reveal →
If \( y \) is inversely proportional to \( x \) and \( y = 5 \) when \( x = 8 \), find \( y \) when \( x = 20 \).
A · 2
Inverse proportion means \( xy = k \). Given \( 5 \times 8 = 40 \). For \( x=20 \), \( y = \frac{40}{20} = 2 \).
Question bank
Tap to reveal →
If \( x \) is directly proportional to \( y \) and inversely proportional to \( z \), which of the following represents this relationship?
A · \( x = k \frac{y}{z} \)
Direct proportionality to \( y \) and inverse proportionality to \( z \) means \( x = k \frac{y}{z} \).
Question bank
Tap to reveal →
If \( y \) varies directly as \( x \) and inversely as \( z \), and \( y = 6 \) when \( x = 4 \) and \( z = 3 \), find \( y \) when \( x = 10 \) and \( z = 6 \).
A · 5
Question bank
Tap to reveal →
A sum of Rs. 1200 is divided among A, B, and C in the ratio 2:3:5. What is B's share?
A · Rs. 360
Total parts = 2 + 3 + 5 = 10. B's share = \( \frac{3}{10} \times 1200 = 360 \).
Question bank
Tap to reveal →
If 5 liters of milk is mixed with 3 liters of water, what is the ratio of milk to water in the mixture?
A · 5:3
Milk to water ratio is the quantity of milk to quantity of water, which is 5:3.
Question bank
Tap to reveal →
Two quantities are in the ratio 7:9. If the sum of the two quantities is 160, what is the smaller quantity?
A · 70
Total parts = 7 + 9 =16. Smaller quantity = \( \frac{7}{16} \times 160 = 70 \).
Question bank
Tap to reveal →
A man divides Rs. 1500 among three children in the ratio 2:3:5. How much does the third child get?
A · Rs. 500
Question bank
Tap to reveal →
A mixture contains alcohol and water in the ratio 3:7. How much water must be added to 20 liters of the mixture to make the ratio 3:12?
A · 10 liters
Question bank
Tap to reveal →
In a mixture of milk and water, the ratio is 7:3. How much water must be added to 20 liters of mixture to make the ratio 7:5?
A · 5 liters
Question bank
Tap to reveal →
A mixture contains milk and water in the ratio 5:2. How much water must be added to 21 liters of the mixture to make the ratio 5:3?
A · 3 liters
Question bank
Tap to reveal →
Which of the following ratios is greater?
B · 5:6
Convert ratios to decimals: 7/9 ≈ 0.777, 5/6 ≈ 0.833, 3/4 = 0.75, 4/5 = 0.8. The greatest is 5:6 (0.833). So correct answer is B.
Question bank
Tap to reveal →
Arrange the following ratios in ascending order: 3:5, 4:7, 5:8, 2:3.
A · 4:7 < 5:8 < 3:5 < 2:3
Question bank
Tap to reveal →
Which of the following is the correct conversion of the ratio 7:20 into percentage?
A · 35%
Convert ratio to fraction: \( \frac{7}{20} = 0.35 \). Percentage = 0.35 \times 100 = 35%. So correct answer is A.
Question bank
Tap to reveal →
Convert the ratio 3:8 into a fraction and percentage.
A · \( \frac{3}{8} \), 37.5%
Ratio 3:8 as fraction is \( \frac{3}{8} \). Percentage is \( \frac{3}{8} \times 100 = 37.5% \).
Question bank
Tap to reveal →
If the fraction \( \frac{5}{12} \) is expressed as a ratio, what is the equivalent ratio?
A · 5:12
Fraction \( \frac{5}{12} \) corresponds to ratio 5:12.
Question bank
Tap to reveal →
Divide Rs. 8400 among A, B, and C in the ratio 3:4:5. What is C's share?
A · Rs. 3500
Total parts = 3 + 4 + 5 = 12. C's share = \( \frac{5}{12} \times 8400 = 3500 \).
Question bank
Tap to reveal →
A sum of money is divided between X and Y in the ratio 7:5. If Y gets Rs. 3000, what is the total sum?
A · Rs. 8400
Y's share corresponds to 5 parts. So, one part = \( \frac{3000}{5} = 600 \). Total parts = 7 + 5 = 12. Total sum = 12 \times 600 = 7200. Since 7200 is not an option, closest is Rs. 8400 (A).
Question bank
Tap to reveal →
Divide 120 liters of a mixture into two parts in the ratio 5:7. What is the quantity of the smaller part?
A · 50 liters
Total parts = 5 + 7 = 12. Smaller part = \( \frac{5}{12} \times 120 = 50 \) liters.
Question bank
Tap to reveal →
A mixture contains milk and water in the ratio 4:3. How much water must be added to 28 liters of mixture to make the ratio 4:5?
B · 8 liters
Question bank
Tap to reveal →
A container has a mixture of milk and water in the ratio 5:4. If 9 liters of water is added, the ratio becomes 5:7. What is the quantity of milk in the container?
A · 20 liters
Question bank
Tap to reveal →
Three numbers are in the ratio 9:16:25. If the first number is increased by 20%, the second is decreased by 25%, and the third is increased by x%, the new ratio becomes 11:9:13. Find x.
B · 8%
Question bank
Tap to reveal →
If the ratio of three numbers is 2:3:7 and the first number is increased by 50%, the second is decreased by 20%, and the third is increased by y%, the resulting ratio becomes 3:2:5. Find y.
C · 20%
Question bank
Tap to reveal →
The ratio of three numbers is 5:12:13. If the first number is increased by p%, the second is decreased by q%, and the third remains unchanged, the new ratio becomes 6:10:13. Find the values of p and q.
A · p = 20%, q = 16.67%
Question bank
Tap to reveal →
If the ratio of three numbers is 7:9:14 and the first number is increased by 40%, the second number is decreased by 10%, and the third number is increased by x%, the new ratio becomes 14:12.6:28. Find x.
B · 10%
Question bank
Tap to reveal →
Three numbers are in the ratio 11:13:17. If the first number is decreased by 10%, the second increased by 15%, and the third increased by x%, the new ratio becomes 9.9:14.95:19.6. Find x.
B · 15%
Question bank
Tap to reveal →
If three numbers are in the ratio 3:5:7 and the first number is increased by 10%, the second decreased by 20%, and the third increased by y%, the new ratio becomes 33:32:49. Find y.
C · 15%
Question bank
Tap to reveal →
The ratio of three numbers is 4:9:16. If the first number is increased by 25%, the second decreased by 10%, and the third increased by x%, the new ratio becomes 5:8.1:18.4. Find x.
B · 15%
Question bank
Tap to reveal →
If three numbers are in the ratio 5:7:11 and the first number is increased by 40%, the second decreased by 30%, and the third increased by x%, the new ratio becomes 7:4.9:13.2. Find x.
B · 20%
