ExplanationStarting with 100: after the first change it becomes 175.00, and after the second change it becomes 182.00 — a net change of +82% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
13
What single discount is equivalent to two successive discounts of 16% and 15%?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation110 and 20 share a common factor of 10; dividing both by it gives 11/2.
ArithmeticGMATGREMathematicsPractice Set
15
Does the fraction 26/396 terminate as a decimal, or does it repeat?
Arithmetic - Number Properties
Medium
ExplanationIn lowest terms, 26/396 = 13/198. A fraction terminates only if its denominator (in lowest terms) has no prime factors other than 2 and 5. Here that is not the case, so it repeats (does not terminate).
ArithmeticGMATGREMathematicsPractice Set
16
If an integer n leaves a remainder of 11 when divided by 12, what is the remainder when (n + 3) is divided by 12?
Arithmetic - Number Properties
Medium
Explanation(n + 3) ≡ (11 + 3) = 14 (mod 12), which leaves remainder 2 when divided by 12.
ArithmeticGMATGREMathematicsPractice Set
17
Simplify the ratio 165:195 to its lowest terms.
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation165 and 195 share a common factor of 15; dividing both by it gives 11:13.
ArithmeticGMATGREMathematicsPractice Set
18
What is the solution set of |x + 30| > 26?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x + 30| > 26 means x is farther than 26 from -30, giving x < -56 or x > -4.
ArithmeticGMATGREMathematicsPractice Set
19
What is the simple interest on Rs. 1217 at 3% per annum for 3 years?
ExplanationStarting with 100: after the first change it becomes 80.00, and after the second change it becomes 51.20 — a net change of -48.8% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
60
What is 105.39 + 19.2?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation105.39 + 19.2 = 124.59.
ArithmeticGMATGREMathematicsPractice Set
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61
What is 58.01 + 63.17?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation58.01 + 63.17 = 121.18.
ArithmeticGMATGREMathematicsPractice Set
62
A shopkeeper marks up an item costing Rs. 55 by 3%. What is the markup amount (in Rs.)?
ExplanationStarting with 100: after the first change it becomes 130.00, and after the second change it becomes 52.00 — a net change of -48% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
67
What is 5/11 of 550?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation5/11 of 550 = (5 × 550) / 11 = 250.
ArithmeticGMATGREMathematicsPractice Set
68
What is the simple interest on Rs. 9277 at 15% per annum for 1 year?
ExplanationUsing the alternating digit-sum rule for 11, the result is 11, which is a multiple of 11, so the answer is Yes.
ArithmeticGMATGREMathematicsPractice Set
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71
What are the solutions to |x| + 21 = 45?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|x| + 21 = 45 means |x| = 24, so x = 24 or x = -24.
ArithmeticGMATGREMathematicsPractice Set
72
For a = 11 and b = 27, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|a + b| = 38 and |a| + |b| = 38. Since a and b have the same sign, the two are equal.
ArithmeticGMATGREMathematicsPractice Set
73
Does the fraction 13/488 terminate as a decimal, or does it repeat?
Arithmetic - Number Properties
Medium
ExplanationIn lowest terms, 13/488 = 13/488. A fraction terminates only if its denominator (in lowest terms) has no prime factors other than 2 and 5. Here that is not the case, so it repeats (does not terminate).
ArithmeticGMATGREMathematicsPractice Set
74
For a = 19 and b = -17, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|a + b| = 2 and |a| + |b| = 36. Since a and b have opposite signs, the two are not equal, with |a+b| smaller.
ArithmeticGMATGREMathematicsPractice Set
75
Is 323 a prime number?
Arithmetic - Number Properties
Medium
Explanation323 is divisible by at least one number between 2 and 322, so it is not prime.
ArithmeticGMATGREMathematicsPractice Set
76
For a = 12 and b = 12, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation|a + b| = 24 and |a| + |b| = 24. Since a and b have the same sign, the two are equal.
ArithmeticGMATGREMathematicsPractice Set
77
What single discount is equivalent to two successive discounts of 15% and 15%?
ExplanationAn absolute value can never equal a negative number, so |x + 38| = −21 has no solution.
ArithmeticGMATGREMathematicsPractice Set
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81
How many multiples of 15 are there between 35 and 154, inclusive?
Arithmetic - Number Properties
Medium
ExplanationThe multiples of 15 in this range run from 45 to 150, giving 8 multiples.
ArithmeticGMATGREMathematicsPractice Set
82
Three warning lights flash every 6, 17, and 12 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, 17, 12) = 204 seconds.
ArithmeticGMATGREMathematicsPractice Set
83
A value is first increased by 28% and then decreased by 16%. What is the overall net percentage change?
ExplanationStarting with 100: after the first change it becomes 128.00, and after the second change it becomes 107.52 — a net change of +7.52% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
84
What is the reciprocal of 10/3?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationThe reciprocal of 10/3 is 3/10, since (10/3) × (3/10) = 1.
ArithmeticGMATGREMathematicsPractice Set
85
What is 72.1 ÷ 10.3?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation72.1 ÷ 10.3 = 7.0.
ArithmeticGMATGREMathematicsPractice Set
86
How many solutions does |x − 15| = −21 have?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationAn absolute value can never equal a negative number, so |x − 15| = −21 has no solution.
ArithmeticGMATGREMathematicsPractice Set
87
What is 90.1 ÷ 10.6?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation90.1 ÷ 10.6 = 8.5.
ArithmeticGMATGREMathematicsPractice Set
88
A shopkeeper marks up an item costing Rs. 1494 by 60%. What is the markup amount (in Rs.)?