ExplanationThe number of digits of 9^37 is floor(37 × log10(9)) + 1 = 36.
ArithmeticGMATGREMathematicsPractice Set
22
What is the highest power of 7 that divides 42! (42 factorial) exactly?
Arithmetic - Number Properties
Medium
ExplanationUsing Legendre's formula, the exponent of 7 in 42! is floor(42/7) + floor(42/49) + ... = 6.
ArithmeticGMATGREMathematicsPractice Set
23
What is the remainder when 893 is divided by 12?
Arithmetic - Number Properties
Medium
Explanation893 = 12 × 74 + 5, so the remainder is 5.
ArithmeticGMATGREMathematicsPractice Set
24
Which is greater: 9/2 or 5?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation9/2 = 4.5000 and 5 = 5.0000, so 5 is greater.
ArithmeticGMATGREMathematicsPractice Set
25
The ratio of boys to girls in a class is 15:14. If there are 300 boys, how many girls are there?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationSince boys:girls = 15:14 and there are 300 boys, each 'part' = 300/15 = 20, so girls = 14 × 20 = 280.
ArithmeticGMATGREMathematicsPractice Set
26
Three warning lights flash every 20, 15, and 17 seconds respectively. If they all flash together at the same instant, after how many seconds will they next flash together?
Arithmetic - Number Properties
Medium
ExplanationThey will next flash together after LCM(20, 15, 17) = 1020 seconds.
ArithmeticGMATGREMathematicsPractice Set
27
What is 2/9 of 252?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation2/9 of 252 = (2 × 252) / 9 = 56.
ArithmeticGMATGREMathematicsPractice Set
28
What is the simple interest on Rs. 19391 at 10% per annum for 7 years?
If 14 pens cost Rs. 308, how much would 21 pens cost?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationCost per pen = Rs. 308/14 = Rs. 22. So 21 pens cost 21 × Rs. 22 = Rs. 462.
ArithmeticGMATGREMathematicsPractice Set
30
Two buses leave a station together. One returns to the station every 13 minutes and the other every 40 minutes. After how many minutes will both buses be at the station together again?
Arithmetic - Number Properties
Medium
ExplanationBoth buses will be at the station together again after LCM(13, 40) = 520 minutes.
ArithmeticGMATGREMathematicsPractice Set
— Sponsored —
31
What is 4/9 + 1/3?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationUsing a common denominator, 4/9 + 1/3 = 7/9.
ExplanationStarting with 100: after the first change it becomes 148.00, and after the second change it becomes 214.60 — a net change of +114.6% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
53
What is the solution set of |x − 16| > 9?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x − 16| > 9 means x is farther than 9 from 16, giving x < 7 or x > 25.
ArithmeticGMATGREMathematicsPractice Set
54
What is the smallest positive integer that leaves a remainder of 11 when divided by 15 and a remainder of 10 when divided by 14?
Arithmetic - Number Properties
Medium
ExplanationSince both remainders are exactly 4 less than their divisors, the answer is LCM(15, 14) − 4 = 210 − 4 = 206.
ArithmeticGMATGREMathematicsPractice Set
55
What is 45.36 ÷ 8.4?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation45.36 ÷ 8.4 = 5.4.
ArithmeticGMATGREMathematicsPractice Set
56
A value is first decreased by 20% and then decreased by 4%. What is the overall net percentage change?
ExplanationStarting with 100: after the first change it becomes 80.00, and after the second change it becomes 76.80 — a net change of -23.2% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
57
What is 8.3 × 13.2?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation8.3 × 13.2 = 109.56.
ArithmeticGMATGREMathematicsPractice Set
58
What is |-56 ÷ 7|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|-56 ÷ 7| = |-56| ÷ |7| = 56 ÷ 7 = 8.
ArithmeticGMATGREMathematicsPractice Set
59
Three warning lights flash every 6, 4, and 8 seconds respectively. If they all flash together at the same instant, after how many seconds will they next flash together?
Arithmetic - Number Properties
Medium
ExplanationThey will next flash together after LCM(6, 4, 8) = 24 seconds.
ArithmeticGMATGREMathematicsPractice Set
60
What is the distance between 78 and -87 on the number line?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationThe distance between two points on a number line is |78 − (-87)| = 165.
ArithmeticGMATGREMathematicsPractice Set
— Sponsored —
61
A shop offers successive discounts of 60% and 40% on an item marked at Rs. 100. What is the final selling price?
Three warning lights flash every 11, 16, and 7 seconds respectively. If they all flash together at the same instant, after how many seconds will they next flash together?
Arithmetic - Number Properties
Medium
ExplanationThey will next flash together after LCM(11, 16, 7) = 1232 seconds.
ArithmeticGMATGREMathematicsPractice Set
63
Which is farther from 23 on the number line: 24 or 65?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationDistance from 23: |24 − 23| = 1, and |65 − 23| = 42. So 65 is farther.
ArithmeticGMATGREMathematicsPractice Set
64
What is the compound interest on Rs. 5625 at 16% per annum, compounded annually, for 2 years?
ExplanationStarting with 100: after the first change it becomes 72.00, and after the second change it becomes 28.80 — a net change of -71.2% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
69
What is 6.0 × 16.9?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation6.0 × 16.9 = 101.4.
ArithmeticGMATGREMathematicsPractice Set
70
What is the simple interest on Rs. 1683 at 6% per annum for 5 years?
How many trailing zeros are in 47! (47 factorial)?
Arithmetic - Number Properties
Medium
ExplanationTrailing zeros come from factors of 5 in 47!. Counting multiples of 5, 25, 125, ... gives 10 trailing zeros.
ArithmeticGMATGREMathematicsPractice Set
99
Which is greater: |53| or |75|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|53| = 53 and |75| = 75, so |75| is greater.
ArithmeticGMATGREMathematicsPractice Set
100
22^2 = 484. How many positive divisors does 484 have?
Arithmetic - Number Properties
Medium
Explanation484 = 2^2 × 11^2, giving 9 divisors — always an odd count for a perfect square, since every divisor pairs with another except the square root.