ExplanationA trinomial x^2 + bx + c is a perfect square exactly when c = (b/2)^2. Here (b/2)^2 = (9)^2 = 81, which does not match c = 70, so it is not a perfect square trinomial.
AlgebraGMATGREMathematicsPractice Set
14
In an arithmetic sequence, the 4th term is 7 and the 17th term is -45. What is the 23rd term?
Algebra - Functions and Sequences (including word…
Medium
Explanationd = (-45 − 7)/(17−4) = -4. Then the 23rd term = 7 + (23−4)(-4) = -69.
AlgebraGMATGREMathematicsPractice Set
15
Two buses leave a station together. One returns to the station every 23 minutes and the other every 7 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(23, 7) = 161 minutes.
ArithmeticGMATGREMathematicsPractice Set
16
Simplify: 7^8 × 7^7
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationWhen multiplying powers with the same base, add the exponents: 7^8 × 7^7 = 7^(8+7) = 7^15.
AntonymsGMATGREMathematicsPractice Set
17
Solve for x: -10x + 16 < -84
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationDividing both sides by the negative coefficient -10 reverses the inequality sign, giving x > 10.
AlgebraGMATGREMathematicsPractice Set
18
What is 4/5 + 7/12?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationUsing a common denominator, 4/5 + 7/12 = 83/60.
ExplanationStarting with 100: after the first change it becomes 72.00, and after the second change it becomes 86.40 — a net change of -13.6% from the original 100.
ArithmeticGMATGREMathematicsPractice Set
48
What is 10.5 × 3.6?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
Explanation10.5 × 3.6 = 37.8.
ArithmeticGMATGREMathematicsPractice Set
49
Rs. 17323 is invested at 8% simple interest per annum for 4 years. What is the total amount after 4 years?
Which of the following numbers lies between -3 and 26?
Artithmetic - Absolute Value and Number Lines
Medium
Explanation10 lies strictly between -3 and 26, while the other options fall outside that range.
ArithmeticGMATGREMathematicsPractice Set
60
Solve for x: x + 33 = 60
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanationx = 60 − (33) = 27, so x = 27/1 = 27.
AlgebraGMATGREMathematicsPractice Set
— Sponsored —
61
What is the smallest positive number that must be added to 7843 so that the sum is exactly divisible by 15?
Arithmetic - Number Properties
Medium
Explanation7843 divided by 15 leaves remainder 13, so adding 15 − 13 = 2 makes it exactly divisible by 15.
ArithmeticGMATGREMathematicsPractice Set
62
What is (2/5)^3 equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation(2/5)^3 = 2^3/5^3 = 8/125.
AntonymsGMATGREMathematicsPractice Set
63
A rectangle has length (x + 4) and width (x + 7). If the area of the rectangle is 70 square units, what is the value of x (where x is a positive number)?
ExplanationThe discriminant is b^2 − 4ac = (-20)^2 − 4(1)(16) = 336, which is positive, so the equation has two distinct real roots.
AlgebraGMATGREMathematicsPractice Set
75
Solve for x: -78 < 4x + 2 < -26
Algebra - Linear equations (1 and 2 variables) an…
Medium
ExplanationSubtracting 2 from all parts: -80 < 4x < -28. Dividing by 4: -20 < x < -7.
AlgebraGMATGREMathematicsPractice Set
76
What is |-199|?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationAbsolute value gives the distance from 0, which is always non-negative, so |-199| = 199.
ArithmeticGMATGREMathematicsPractice Set
77
What is (5.7 × 10^6) × (7.3 × 10^6) in scientific notation?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationMultiply the mantissas (5.7 × 7.3 = 41.61) and add the exponents (6 + 6 = 13), adjusting so the mantissa stays between 1 and 10: 4.16 × 10^13.
AntonymsGMATGREMathematicsPractice Set
78
Rs. 19901 is invested at 12.5% simple interest per annum for 4 years. What is the total amount after 4 years?
Which is farther from -5 on the number line: -33 or 31?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationDistance from -5: |-33 − (-5)| = 28, and |31 − (-5)| = 36. So 31 is farther.
ArithmeticGMATGREMathematicsPractice Set
90
In an arithmetic sequence, the 7th term is -34 and the 13th term is -88. What is the 27th term?
Algebra - Functions and Sequences (including word…
Medium
Explanationd = (-88 − (-34))/(13−7) = -9. Then the 27th term = -34 + (27−7)(-9) = -214.
AlgebraGMATGREMathematicsPractice Set
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91
How many prime numbers are there between 3 and 18, inclusive?
Arithmetic - Number Properties
Medium
ExplanationThe primes between 3 and 18 are [3, 5, 7, 11, 13, 17], totaling 6.
ArithmeticGMATGREMathematicsPractice Set
92
What is (7/15)^4 equal to?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
Explanation(7/15)^4 = 7^4/15^4 = 2401/50625.
AntonymsGMATGREMathematicsPractice Set
93
The ratio of boys to girls in a class is 5:2. If there are 195 boys, how many girls are there?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationSince boys:girls = 5:2 and there are 195 boys, each 'part' = 195/5 = 39, so girls = 2 × 39 = 78.
ArithmeticGMATGREMathematicsPractice Set
94
A delivery service charges a fixed fee of Rs. 28 plus Rs. 39 per item. If a customer has a budget of Rs. 903, what is the maximum number of items they can order?
Algebra - Linear equations (1 and 2 variables) an…
Medium
Explanation28 + 39n ≤ 903, so n ≤ 875/39 ≈ 22.44, meaning at most 22 items.
AlgebraGMATGREMathematicsPractice Set
95
What is the midpoint between 3 and -40 on the number line?
Artithmetic - Absolute Value and Number Lines
Medium
ExplanationThe midpoint of 3 and -40 is (3 + -40) / 2 = -37/2 = -37/2.
ArithmeticGMATGREMathematicsPractice Set
96
Which is greater: 11.17 or 7.176?
Arithmetic - Fractions, Decimals, Ratios and Prop…
Medium
ExplanationComparing digit by digit, 11.17 is greater than 7.176.
ArithmeticGMATGREMathematicsPractice Set
97
√8 × √7 is equivalent to which of the following?
Arithmetic - Powers and Roots (Exponents, Scienti…
Medium
ExplanationBy the product rule for radicals, √a × √b = √(ab), so √8 × √7 = √56.
AntonymsGMATGREMathematicsPractice Set
98
40^2 − 32^2 is exactly divisible by which of the following?
Arithmetic - Number Properties
Medium
Explanation40^2 − 32^2 = (40 − 32)(40 + 32) = 8 × 72, so it is always divisible by 8 (and by 72).