Your FREE GMAT (Graduate Management Admission Test) Practice Test 2026 – 420+ Q&A

Quantitative Reasoning (133)

1. The product of any two consecutive integers is always which of the following?

   • A.Odd
   • B.Prime
   • C.Even
   • D.A perfect square
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   Correct answer: Even

   The product is always even. Among any two consecutive integers, one must be even, and a product that includes an even factor is itself even; it need not be prime or a perfect square.

2. Which of the following integers is prime?

   • A.91
   • B.87
   • C.99
   • D.97
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   Correct answer: 97

   The prime number is 97. The value 91 equals $7 \cdot 13$, 87 equals $3 \cdot 29$, and 99 equals $9 \cdot 11$, so each is composite, while 97 has no divisors other than 1 and itself.

3. If $n$ is an odd integer, which of the following must also be odd?

   • A.$n + 1$
   • B.$n^2$
   • C.$2n$
   • D.$3n + 1$
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   Correct answer: $n^2$

   The expression $n^2$ must be odd. The square of an odd number is odd, while $n + 1$ turns it even, $2n$ is even, and $3n + 1$ becomes even when $n$ is odd.

4. When a positive integer is divided by 9, the remainder is 5. What is the remainder when 4 is added to that integer and the result is divided by 9?

   • A.9
   • B.0
   • C.1
   • D.4
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   Correct answer: 0

   The remainder is 0. The integer equals $9q + 5$, so adding 4 gives $9q + 9 = 9(q + 1)$, which is a multiple of 9 and therefore leaves no remainder.

5. Which of the following numbers is divisible by both 6 and 8?

   • A.48
   • B.36
   • C.56
   • D.60
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   Correct answer: 48

   The number 48 is divisible by both. A number divisible by 6 and 8 must be a multiple of their least common multiple, 24, and only 48 among the choices is a multiple of 24.

6. How many positive divisors does 100 have?

   • A.6
   • B.8
   • C.10
   • D.9
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   Correct answer: 9

   The answer is 9. The prime factorization of 100 is $2^2 \cdot 5^2$, and the divisor count equals $(2 + 1)(2 + 1) = 9$.

7. Expressed as a product of primes, what is 90?

   • A.$2 \cdot 3^2 \cdot 5$
   • B.$2 \cdot 45$
   • C.$2 \cdot 3 \cdot 15$
   • D.$3 \cdot 30$
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   Correct answer: $2 \cdot 3^2 \cdot 5$

   The prime factorization is $2 \cdot 3^2 \cdot 5$. Breaking 90 down into primes gives $2 \cdot 3 \cdot 3 \cdot 5$; the other options still contain composite numbers such as 15, 45, or 30.

8. Using prime factorization, what is the least common multiple of 8 and 20?

   • A.4
   • B.40
   • C.80
   • D.160
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   Correct answer: 40

   The least common multiple is 40. Factoring gives $8 = 2^3$ and $20 = 2^2 \cdot 5$; taking the highest power of each prime yields $2^3 \cdot 5 = 40$.

9. What is $\frac{5}{6}$ minus $\frac{1}{4}$ written as a single fraction in lowest terms?

   • A.$\frac{4}{2}$
   • B.$\frac{6}{10}$
   • C.$\frac{7}{12}$
   • D.$\frac{1}{2}$
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   Correct answer: $\frac{7}{12}$

   The result is $\frac{7}{12}$. Converting to a common denominator of 12 gives $\frac{10}{12}$ minus $\frac{3}{12} = \frac{7}{12}$, which cannot be reduced further because 7 is prime and does not divide 12.

10. What is 0.6 expressed as a fraction in lowest terms?

    • A.$\frac{6}{10}$
    • B.$\frac{2}{3}$
    • C.$\frac{3}{5}$
    • D.$\frac{1}{6}$
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    Correct answer: $\frac{3}{5}$

    The fraction is $\frac{3}{5}$. Writing 0.6 as $\frac{6}{10}$ and dividing numerator and denominator by their common factor of 2 gives $\frac{3}{5}$.

11. What percent of 250 is 40?

    • A.12 percent
    • B.40 percent
    • C.25 percent
    • D.16 percent
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    Correct answer: 16 percent

    The answer is 16 percent. Dividing 40 by 250 gives 0.16, which converts to 16 percent.

12. A jacket originally priced at 80 dollars is marked down by 25 percent. What is the sale price?

    • A.55 dollars
    • B.65 dollars
    • C.60 dollars
    • D.75 dollars
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    Correct answer: 60 dollars

    The sale price is 60 dollars. A 25 percent markdown removes $0.25 \cdot 80$, which is 20 dollars, leaving $80 - 20 = 60$ dollars.

13. A merchant sells an item for 150 dollars at a 50 percent profit over cost. What was the cost?

    • A.75 dollars
    • B.112.50 dollars
    • C.100 dollars
    • D.125 dollars
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    Correct answer: 100 dollars

    The cost was 100 dollars. A 50 percent profit means the selling price equals $1.5$ times the cost, so dividing 150 by 1.5 gives a cost of 100 dollars.

14. If 2,500 dollars earns 200 dollars in simple interest over 2 years, what is the annual interest rate?

    • A.4 percent
    • B.2 percent
    • C.8 percent
    • D.10 percent
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    Correct answer: 4 percent

    The rate is 4 percent. Simple interest equals principal times rate times time, so $200 = 2500 \cdot r \cdot 2$, giving $r = 200 \div 5000 = 0.04$, or 4 percent.

15. The ratio of red to blue tiles is 4 to 7. If there are 35 blue tiles, how many red tiles are there?

    • A.20
    • B.15
    • C.28
    • D.49
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    Correct answer: 20

    There are 20 red tiles. Each ratio unit equals $35 \div 7$, which is 5 tiles, so the 4 units of red tiles equal $4 \cdot 5 = 20$.

16. If 6 pens cost 9 dollars, how much do 10 pens cost at the same rate?

    • A.12 dollars
    • B.13.50 dollars
    • C.16.50 dollars
    • D.15 dollars
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    Correct answer: 15 dollars

    Ten pens cost 15 dollars. The unit price is $9 \div 6$, which is 1.50 dollars per pen, and $10 \cdot 1.50$ equals 15 dollars.

17. In a ratio of 2 to 3 to 5, the three parts of a 60-unit total are split. What is the size of the largest part?

    • A.12
    • B.30
    • C.18
    • D.36
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    Correct answer: 30

    The largest part is 30. The ratio has $2 + 3 + 5 = 10$ units, so each unit equals $60 \div 10 = 6$, and the largest share of 5 units equals $5 \cdot 6 = 30$.

18. What is the value of $3^3 \cdot 3^2$?

    • A.$3^6$
    • B.$3^5$
    • C.$9^5$
    • D.27
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    Correct answer: $3^5$

    The value is $3^5$. When multiplying powers with the same base, add the exponents, so $3^{(3 + 2)}$ equals $3^5$.

19. What is $\sqrt[3]{64}$?

    • A.2
    • B.4
    • C.8
    • D.16
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    Correct answer: 4

    $\sqrt[3]{64}$ is 4. Since $4 \cdot 4 \cdot 4$ equals 64, the number whose cube is 64 is 4.

20. What is the value of $10^0$?

    • A.0
    • B.Undefined
    • C.10
    • D.1
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    Correct answer: 1

    The value is 1. Any nonzero base raised to the zero power equals 1 by the rules of exponents.

21. If $4x + 9$ equals 33, what is the value of $x$?

    • A.4
    • B.10.5
    • C.8
    • D.6
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    Correct answer: 6

    The value of $x$ is 6. Subtracting 9 from both sides gives $4x = 24$, and dividing both sides by 4 yields $x = 6$.

22. A gym charges a 30-dollar sign-up fee plus 25 dollars per month. After how many months does the total cost reach 180 dollars?

    • A.5 months
    • B.6 months
    • C.7 months
    • D.8 months
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    Correct answer: 6 months

    The total reaches 180 dollars after 6 months. Setting up $30 + 25m = 180$ and subtracting 30 gives $25m = 150$, so $m = 6$.

23. If $2x - 3y$ equals 12 and $x$ equals 9, what is the value of $y$?

    • A.9
    • B.3
    • C.6
    • D.2
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    Correct answer: 2

    The value of $y$ is 2. Substituting $x = 9$ gives $18 - 3y = 12$, so $3y = 6$ and $y = 2$.

24. What are the solutions to $x^2 + 2x - 15 = 0$?

    • A.$x = 3$ and $x = 5$
    • B.$x = -3$ and $x = 5$
    • C.$x = 3$ and $x = -5$
    • D.$x = -3$ and $x = -5$
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    Correct answer: $x = 3$ and $x = -5$

    The solutions are $x = 3$ and $x = -5$. The expression factors as $(x - 3)(x + 5)$, whose roots multiply to $-15$ and add to 2.

25. If $x^2 - 8x = 0$, what are the solutions for $x$?

    • A.$x = 0$ and $x = -8$
    • B.$x = 8$ only
    • C.$x = -8$ and $x = 8$
    • D.$x = 0$ and $x = 8$
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    Correct answer: $x = 0$ and $x = 8$

    The solutions are $x = 0$ and $x = 8$. Factoring gives $x(x - 8) = 0$, so either $x = 0$ or $x = 8$ satisfies the equation.

26. The product of two numbers is 24 and their sum is 11. What are the two numbers?

    • A.2 and 12
    • B.3 and 8
    • C.4 and 6
    • D.1 and 24
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    Correct answer: 3 and 8

    The two numbers are 3 and 8. They are roots of $x^2 - 11x + 24 = 0$, which factors as $(x - 3)(x - 8)$, and only 3 and 8 both sum to 11 and multiply to 24.

27. Which of the following describes the solution to $5x - 4 \le 16$?

    • A.$x \le 4$
    • B.$x \ge 4$
    • C.$x \le 20$
    • D.$x \ge 20$
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    Correct answer: $x \le 4$

    The solution is $x \le 4$. Adding 4 to both sides gives $5x \le 20$, and dividing by the positive 5 keeps the direction, yielding $x \le 4$.

28. If $7 - 2x > 1$, which of the following describes $x$?

    • A.$x > 4$
    • B.$x > 3$
    • C.$x < 4$
    • D.$x < 3$
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    Correct answer: $x < 3$

    The solution is $x < 3$. Subtracting 7 gives $-2x > -6$, and dividing by $-2$ reverses the inequality to $x < 3$.

29. For which values of $x$ is the statement $4x > 2x + 10$ true?

    • A.$x < 5$
    • B.$x > 5$
    • C.$x > 10$
    • D.$x < 10$
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    Correct answer: $x > 5$

    The statement is true when $x > 5$. Subtracting $2x$ from both sides gives $2x > 10$, and dividing by 2 yields $x > 5$.

30. What is the value of the absolute value of (negative 7) plus the absolute value of 3?

    • A.4
    • B.Negative 4
    • C.10
    • D.Negative 10
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    Correct answer: 10

    The value is 10. The absolute value of $-7$ is 7 and the absolute value of 3 is 3, and adding these nonnegative distances gives 10.

31. Which values of $x$ satisfy the equation $|x - 2| = 5$?

    • A.$x = 7$ and $x = -3$
    • B.$x = 3$ and $x = -7$
    • C.$x = 7$ only
    • D.$x = -3$ only
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    Correct answer: $x = 7$ and $x = -3$

    The solutions are $x = 7$ and $x = -3$. The expression inside can equal either 5 or $-5$, so $x - 2 = 5$ gives $x = 7$ and $x - 2 = -5$ gives $x = -3$.

32. Simplify the expression $3(x - 2) + 2(x + 4)$.

    • A.$6x + 2$
    • B.$5x - 2$
    • C.$5x + 14$
    • D.$5x + 2$
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    Correct answer: $5x + 2$

    The simplified form is $5x + 2$. Distributing gives $3x - 6 + 2x + 8$, and combining like terms produces $5x + 2$.

33. Which of the following is the expanded form of $(x + 4)^2$?

    • A.$x^2 + 16$
    • B.$x^2 + 4x + 16$
    • C.$x^2 + 8x + 16$
    • D.$x^2 + 8x + 8$
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    Correct answer: $x^2 + 8x + 16$

    The expansion is $x^2 + 8x + 16$. Squaring a binomial gives the first term squared, twice the product of the terms, and the last term squared, so the middle term is $2 \cdot 4 \cdot x = 8x$.

34. Which expression is equivalent to $(6x^2 + 9x) \div 3x$, for $x \ne 0$?

    • A.$6x + 9$
    • B.$2x^2 + 3$
    • C.$2x + 3$
    • D.$2x + 9$
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    Correct answer: $2x + 3$

    The simplified expression is $2x + 3$. Dividing each term by $3x$ gives $6x^2 \div 3x = 2x$ and $9x \div 3x = 3$, so the result is $2x + 3$.

35. If $h(x) = x^2 + 2x$, what is the value of $h(4)$?

    • A.24
    • B.20
    • C.16
    • D.32
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    Correct answer: 24

    The value is 24. Substituting 4 for $x$ gives $16 + 8$, which equals 24.

36. If $f(x) = 3x - 5$ and $g(x) = x + 2$, what is the value of $f(g(3))$?

    • A.10
    • B.4
    • C.14
    • D.16
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    Correct answer: 10

    The value is 10. First $g(3) = 3 + 2 = 5$, then $f(5) = 3 \cdot 5 - 5 = 15 - 5 = 10$.

37. If $f(x) = 2x + 1$, what is the value of $f(a + 1)$ in terms of $a$?

    • A.$2a + 1$
    • B.$2a + 3$
    • C.$2a + 2$
    • D.$2a$
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    Correct answer: $2a + 3$

    The value is $2a + 3$. Substituting $a + 1$ for $x$ gives $2(a + 1) + 1 = 2a + 2 + 1 = 2a + 3$.

38. A printer can print 50 pages in 2 minutes. How many minutes does it take to print 375 pages at the same rate?

    • A.12 minutes
    • B.18 minutes
    • C.15 minutes
    • D.20 minutes
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    Correct answer: 15 minutes

    It takes 15 minutes. The printer's rate is $50 \div 2 = 25$ pages per minute, and $375 \div 25$ equals 15 minutes.

39. If 3 workers can complete a task in 8 hours, how long would it take 6 workers to complete the same task, assuming equal work rates?

    • A.2 hours
    • B.16 hours
    • C.12 hours
    • D.4 hours
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    Correct answer: 4 hours

    It takes 4 hours. Doubling the number of workers halves the time, so 8 hours divided by 2 equals 4 hours.

40. One pipe drains a pool in 4 hours while a second pipe drains it in 6 hours. Working together, how long does it take to drain the pool?

    • A.2 hours
    • B.10 hours
    • C.5 hours
    • D.2.4 hours
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    Correct answer: 2.4 hours

    It takes 2.4 hours. The combined draining rate is $\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$ of the pool per hour, so the time is the reciprocal, $\frac{12}{5} = 2.4$ hours.

41. A cyclist rides 45 miles in 3 hours. What is the cyclist's average speed?

    • A.12 miles per hour
    • B.15 miles per hour
    • C.18 miles per hour
    • D.135 miles per hour
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    Correct answer: 15 miles per hour

    The average speed is 15 miles per hour. Dividing distance by time gives $45 \div 3$, which equals 15 miles per hour.

42. A runner travels at 8 miles per hour for 45 minutes. How many miles does the runner cover?

    • A.6 miles
    • B.4 miles
    • C.8 miles
    • D.12 miles
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    Correct answer: 6 miles

    The runner covers 6 miles. Converting 45 minutes to 0.75 hours and multiplying by the speed gives $8 \cdot 0.75 = 6$ miles.

43. Two cars leave the same point traveling toward each other from 300 miles apart, one at 40 miles per hour and the other at 60 miles per hour. After how many hours do they meet?

    • A.2 hours
    • B.5 hours
    • C.3 hours
    • D.6 hours
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    Correct answer: 3 hours

    They meet after 3 hours. Moving toward each other, they close the gap at the combined speed of 100 miles per hour, so $300 \div 100$ equals 3 hours.

44. How many liters of pure water must be added to 12 liters of a 40 percent salt solution to dilute it to a 30 percent salt solution?

    • A.4 liters
    • B.3 liters
    • C.6 liters
    • D.8 liters
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    Correct answer: 4 liters

    You must add 4 liters. The amount of salt stays at $0.40 \cdot 12 = 4.8$ liters, so $4.8 = 0.30(12 + x)$ gives $12 + x = 16$, meaning $x = 4$ liters of water.

45. A 60-pound trail mix is 30 percent raisins by weight. How many pounds of raisins does it contain?

    • A.18 pounds
    • B.12 pounds
    • C.20 pounds
    • D.24 pounds
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    Correct answer: 18 pounds

    It contains 18 pounds of raisins. Taking 30 percent of 60 pounds gives $0.30 \cdot 60$, which equals 18 pounds.

46. A 20 percent alcohol solution is mixed with a 60 percent alcohol solution to make 20 liters of a 45 percent solution. How many liters of the 60 percent solution are used?

    • A.5 liters
    • B.7.5 liters
    • C.15 liters
    • D.12.5 liters
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    Correct answer: 12.5 liters

    The mixture uses 12.5 liters of the 60 percent solution. With $x$ liters at 60 percent and $(20 - x)$ at 20 percent, the balance $0.60x + 0.20(20 - x) = 0.45(20)$ gives $0.40x = 5$, so $x = 12.5$ liters.

47. In a group of 40 employees, 25 speak English and 18 speak Spanish, while every employee speaks at least one of the two languages. How many speak both?

    • A.7
    • B.5
    • C.3
    • D.13
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    Correct answer: 3

    Three employees speak both. Since everyone speaks at least one language, the overlap equals $25 + 18 - 40 = 3$.

48. In how many distinct ways can the letters of the word LOGIC be arranged, given that all five letters are different?

    • A.120
    • B.60
    • C.25
    • D.625
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    Correct answer: 120

    There are 120 arrangements. Ordering 5 distinct letters is $5!$, which equals $5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 120$.

49. A bag holds 3 green, 2 yellow, and 5 black marbles. If one marble is drawn at random, what is the probability that it is not black?

    • A.$\frac{2}{5}$
    • B.$\frac{1}{2}$
    • C.$\frac{1}{5}$
    • D.$\frac{3}{10}$
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    Correct answer: $\frac{1}{2}$

    The probability is $\frac{1}{2}$. There are 10 marbles and 5 are not black (3 green plus 2 yellow), so $\frac{5}{10}$ reduces to $\frac{1}{2}$.

50. If $k$ is a positive integer, which of the following expressions is always odd?

    • A.$k^2 + k$
    • B.$2k + 1$
    • C.$4k - 2$
    • D.$k \cdot (k + 1)$
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    Correct answer: $2k + 1$

    The expression $2k + 1$ is always odd. The term $2k$ is even for any integer $k$, and adding 1 makes it odd; the other expressions are even because each contains a guaranteed even factor or sum.

51. How many prime numbers are there between 20 and 30, inclusive?

    • A.2
    • B.1
    • C.3
    • D.4
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    Correct answer: 2

    There are 2 primes in that range, namely 23 and 29. The remaining values from 20 to 30 are all composite, so exactly two qualify.

52. What is the units digit of $7^4$?

    • A.3
    • B.7
    • C.9
    • D.1
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    Correct answer: 1

    The units digit is 1. Powers of 7 cycle through units digits 7, 9, 3, 1, and the 4th power lands on 1.

53. If the product of two positive integers is odd, what must be true of the two integers?

    • A.Both are even
    • B.Both are odd
    • C.One is even and one is odd
    • D.Both are prime
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    Correct answer: Both are odd

    Both integers must be odd. A product is odd only when no factor is even, so each of the two integers has to be odd.

54. When a positive integer is divided by 5, the remainder is 3. What is the remainder when 7 is added to that integer and the result is divided by 5?

    • A.0
    • B.1
    • C.2
    • D.3
    Show answerHide answer

    Correct answer: 0

    The remainder is 0. The integer equals $5q + 3$, so adding 7 gives $5q + 10$, which is $5 \cdot (q + 2)$ and leaves no remainder.

55. Which of the following numbers is divisible by 12?

    • A.66
    • B.90
    • C.108
    • D.138
    Show answerHide answer

    Correct answer: 108

    The number 108 is divisible by 12, since 108 equals $12 \cdot 9$. The others are not multiples of 12 because they fail the test for divisibility by 4 or by 3.

56. How many positive divisors does 48 have?

    • A.8
    • B.9
    • C.12
    • D.10
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    Correct answer: 10

    The number 48 has 10 positive divisors. Since 48 equals $2^4 \cdot 3$, the count is $(4 + 1) \cdot (1 + 1)$, which is 10.

57. What is the greatest common divisor of 54 and 72?

    • A.6
    • B.9
    • C.12
    • D.18
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    Correct answer: 18

    The greatest common divisor is 18. Both numbers share the factors 2 and $3^2$, whose product 18 is the largest integer dividing both.

58. Expressed as a product of primes, what is 126?

    • A.$2 \cdot 63$
    • B.$2 \cdot 3^2 \cdot 7$
    • C.$2 \cdot 3 \cdot 21$
    • D.$6 \cdot 21$
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    Correct answer: $2 \cdot 3^2 \cdot 7$

    The prime factorization is $2 \cdot 3^2 \cdot 7$. Only this option lists primes exclusively, and their product equals 126.

59. How many distinct prime factors does 210 have?

    • A.2
    • B.3
    • C.4
    • D.5
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    Correct answer: 4

    The number 210 has 4 distinct prime factors. Since 210 equals $2 \cdot 3 \cdot 5 \cdot 7$, the distinct primes are 2, 3, 5, and 7.

60. Using prime factorization, what is the least common multiple of 12 and 18?

    • A.6
    • B.24
    • C.36
    • D.72
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    Correct answer: 36

    The least common multiple is 36. Factoring gives 12 equal to $2^2 \cdot 3$ and 18 equal to $2 \cdot 3^2$, so the highest powers give $2^2 \cdot 3^2$, which is 36.

61. What is $\frac{2}{3} + \frac{1}{5}$ written as a single fraction in lowest terms?

    • A.$\frac{3}{8}$
    • B.$\frac{11}{15}$
    • C.$\frac{13}{15}$
    • D.$\frac{2}{8}$
    Show answerHide answer

    Correct answer: $\frac{13}{15}$

    The sum is $\frac{13}{15}$. Using a common denominator of 15, $\frac{2}{3}$ is $\frac{10}{15}$ and $\frac{1}{5}$ is $\frac{3}{15}$, which add to $\frac{13}{15}$ and cannot be reduced.

62. What is 0.45 expressed as a fraction in lowest terms?

    • A.$\frac{9}{20}$
    • B.$\frac{45}{10}$
    • C.$\frac{4}{9}$
    • D.$\frac{9}{25}$
    Show answerHide answer

    Correct answer: $\frac{9}{20}$

    The value equals $\frac{9}{20}$. Writing 0.45 as $\frac{45}{100}$ and dividing numerator and denominator by 5 gives $\frac{9}{20}$.

63. What percent of 60 is 27?

    • A.35 percent
    • B.40 percent
    • C.50 percent
    • D.45 percent
    Show answerHide answer

    Correct answer: 45 percent

    The answer is 45 percent. Dividing 27 by 60 gives 0.45, which converts to 45 percent.

64. A shirt regularly priced at 45 dollars is marked down by 40 percent. What is the sale price?

    • A.18 dollars
    • B.25 dollars
    • C.27 dollars
    • D.30 dollars
    Show answerHide answer

    Correct answer: 27 dollars

    The sale price is 27 dollars. A 40 percent markdown removes $0.40 \cdot 45$, which is 18 dollars, leaving $45 - 18 = 27$ dollars.

65. A dealer sells a bicycle for 270 dollars at a 35 percent loss on cost. What was the cost?

    • A.365 dollars
    • B.400 dollars
    • C.420 dollars
    • D.415 dollars
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    Correct answer: 415 dollars

    The cost was about 415 dollars. A 35 percent loss means the selling price is 65 percent of cost, so $270 \div 0.65$ is approximately 415 dollars.

66. A deposit of 6,000 dollars earns simple interest at 4 percent per year. How much interest accrues in 5 years?

    • A.900 dollars
    • B.1,000 dollars
    • C.1,200 dollars
    • D.1,500 dollars
    Show answerHide answer

    Correct answer: 1,200 dollars

    The interest is 1,200 dollars. Simple interest equals principal times rate times time, so $6000 \cdot 0.04 \cdot 5 = 1200$ dollars.

67. The ratio of pencils to erasers in a box is 7 to 4. If there are 28 pencils, how many erasers are there?

    • A.16
    • B.12
    • C.18
    • D.20
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    Correct answer: 16

    There are 16 erasers. Each ratio unit equals $28 \div 7$, which is 4, so the 4 units of erasers equal $4 \cdot 4$, or 16.

68. If 5 notebooks cost 12 dollars, how much do 15 notebooks cost at the same rate?

    • A.30 dollars
    • B.32 dollars
    • C.36 dollars
    • D.40 dollars
    Show answerHide answer

    Correct answer: 36 dollars

    Fifteen notebooks cost 36 dollars. Fifteen is three times five, so the cost scales to $3 \cdot 12$, which is 36 dollars.

69. A sum of 120 dollars is split in the ratio 3 to 5 to 4. What is the smallest share?

    • A.24 dollars
    • B.30 dollars
    • C.36 dollars
    • D.40 dollars
    Show answerHide answer

    Correct answer: 30 dollars

    The smallest share is 30 dollars. The ratio has $3 + 5 + 4$ equal to 12 units, each worth 10 dollars, so the smallest share of 3 units equals 30 dollars.

70. What is the value of 2 to the fourth power times 2 cubed?

    • A.2 to the seventh
    • B.2 to the twelfth
    • C.4 to the seventh
    • D.2 to the first
    Show answerHide answer

    Correct answer: 2 to the seventh

    The value is $2^7$. Multiplying powers with the same base adds the exponents, giving $2^{4 + 3}$.

71. What is the value of $\sqrt{196}$?

    • A.12
    • B.13
    • C.14
    • D.16
    Show answerHide answer

    Correct answer: 14

    The value is 14, because $14 \cdot 14 = 196$.

72. What is the value of 3 to the negative second power?

    • A.$\frac{1}{9}$
    • B.$\frac{1}{6}$
    • C.Minus 9
    • D.9
    Show answerHide answer

    Correct answer: $\frac{1}{9}$

    The value is $\frac{1}{9}$. A negative exponent means the reciprocal, so $3^{-2}$ equals 1 over $3^2$, which is $\frac{1}{9}$.

73. If 7x plus 5 equals 47, what is the value of x?

    • A.5
    • B.6
    • C.7
    • D.8
    Show answerHide answer

    Correct answer: 6

    The value of $x$ is 6. Subtracting 5 from both sides gives $7x = 42$, and dividing by 7 yields $x = 6$.

74. A streaming service charges a 12 dollar setup fee plus 8 dollars per month. After how many months does the total cost reach 84 dollars?

    • A.7 months
    • B.8 months
    • C.9 months
    • D.10 months
    Show answerHide answer

    Correct answer: 9 months

    The total reaches 84 dollars after 9 months. Setting up $12 + 8m = 84$ and subtracting 12 gives $8m = 72$, so $m = 9$.

75. If 3x plus 7 equals 2x plus 15, what is the value of x?

    • A.6
    • B.7
    • C.9
    • D.8
    Show answerHide answer

    Correct answer: 8

    The value of $x$ is 8. Subtracting $2x$ from both sides gives $x + 7 = 15$, so $x = 8$.

76. What are the solutions to x squared plus x minus 20 equals 0?

    • A.X equals 4 or minus 5
    • B.X equals minus 4 or 5
    • C.X equals 2 or minus 10
    • D.X equals minus 2 or 10
    Show answerHide answer

    Correct answer: X equals 4 or minus 5

    The solutions are $x = 4$ or $x = -5$. The expression factors as $(x - 4)(x + 5) = 0$, whose roots multiply to $-20$ and add to 1, giving $x = 4$ or $x = -5$.

77. If x squared minus 6x equals 0, what are the solutions for x?

    • A.X equals 0 or 6
    • B.X equals 6 only
    • C.X equals minus 6 or 6
    • D.X equals 0 or minus 6
    Show answerHide answer

    Correct answer: X equals 0 or 6

    The solutions are $x = 0$ or $x = 6$. Factoring gives $x(x - 6) = 0$, so $x$ is 0 or 6.

78. The sum of two numbers is 13 and their product is 40. What are the two numbers?

    • A.4 and 9
    • B.5 and 8
    • C.6 and 7
    • D.3 and 10
    Show answerHide answer

    Correct answer: 5 and 8

    The two numbers are 5 and 8. They are roots of $x^2 - 13x + 40 = 0$, which factors as $(x - 5)(x - 8)$, and only 5 and 8 sum to 13 and multiply to 40.

79. Which of the following describes the solution to 4x plus 3 is less than 19?

    • A.X is less than 4
    • B.X is greater than 4
    • C.X is less than 16
    • D.X is greater than 16
    Show answerHide answer

    Correct answer: X is less than 4

    The solution is $x < 4$. Subtracting 3 gives $4x < 16$, and dividing by the positive 4 gives $x < 4$.

80. If 9 minus 3x is greater than or equal to 0, which of the following describes x?

    • A.X is greater than or equal to 3
    • B.X is less than or equal to 3
    • C.X is greater than or equal to minus 3
    • D.X is less than or equal to minus 3
    Show answerHide answer

    Correct answer: X is less than or equal to 3

    The solution is $x \le 3$. Subtracting 9 gives $-3x \ge -9$, and dividing by $-3$ reverses the inequality to $x \le 3$.

81. If x is an integer and minus 1 is less than x and x is less than 4, what is the sum of all possible values of x?

    • A.3
    • B.4
    • C.6
    • D.10
    Show answerHide answer

    Correct answer: 6

    The sum is 6. The integers strictly between $-1$ and 4 are 0, 1, 2, and 3, which add to 6.

82. What is the value of the absolute value of (minus 12) plus the absolute value of (minus 5)?

    • A.7
    • B.17
    • C.Minus 7
    • D.Minus 17
    Show answerHide answer

    Correct answer: 17

    The value is 17. The absolute value of $-12$ is 12 and of $-5$ is 5, and adding these nonnegative distances gives 17.

83. Which values of x satisfy the equation absolute value of (x minus 4) equals 6?

    • A.X equals 10 or minus 2
    • B.X equals 2 or minus 10
    • C.X equals 10 only
    • D.X equals minus 2 only
    Show answerHide answer

    Correct answer: X equals 10 or minus 2

    The solutions are $x = 10$ or $x = -2$. The expression inside can equal 6 or $-6$, so $x - 4 = 6$ gives 10 and $x - 4 = -6$ gives $-2$.

84. Simplify the expression 4(x plus 3) minus 2(x minus 1).

    • A.2x plus 10
    • B.2x plus 14
    • C.6x plus 10
    • D.2x plus 11
    Show answerHide answer

    Correct answer: 2x plus 14

    The simplified form is $2x + 14$. Distributing gives $4x + 12 - 2x + 2$, and combining like terms produces $2x + 14$.

85. Factor the expression x squared minus 5x minus 14.

    • A.(x minus 2)(x plus 7)
    • B.(x plus 2)(x minus 7)
    • C.(x minus 1)(x plus 14)
    • D.(x plus 1)(x minus 14)
    Show answerHide answer

    Correct answer: (x plus 2)(x minus 7)

    The factorization is $(x + 2)(x - 7)$. These binomials multiply to give a constant of $-14$ and a middle term of $-5x$.

86. If p(x) equals x squared plus 3x minus 2, what is the value of p(4)?

    • A.22
    • B.24
    • C.28
    • D.26
    Show answerHide answer

    Correct answer: 26

    The value is 26. Substituting 4 for $x$ gives $16 + 12 - 2$, which equals 26.

87. If f(x) equals 2x minus 3 and g(x) equals x plus 5, what is the value of g(f(4))?

    • A.8
    • B.10
    • C.12
    • D.14
    Show answerHide answer

    Correct answer: 10

    The value is 10. First $f(4) = 2 \cdot 4 - 3$, which is 5, then $g(5) = 5 + 5$, which is 10.

88. A copier prints 80 pages in 5 minutes. How many minutes does it take to print 400 pages at the same rate?

    • A.20 minutes
    • B.25 minutes
    • C.30 minutes
    • D.35 minutes
    Show answerHide answer

    Correct answer: 25 minutes

    It takes 25 minutes. The rate is $80 \div 5$, which is 16 pages per minute, and $400 \div 16 = 25$ minutes.

89. A car travels at 60 miles per hour for 2 hours and 30 minutes. How far does it travel?

    • A.120 miles
    • B.135 miles
    • C.150 miles
    • D.165 miles
    Show answerHide answer

    Correct answer: 150 miles

    The distance is 150 miles. Two hours and 30 minutes is 2.5 hours, and $60 \cdot 2.5 = 150$ miles.

90. If k is an odd integer, which of the following must be even?

    • A.K + 2
    • B.K squared
    • C.K + k
    • D.5k
    Show answerHide answer

    Correct answer: K + k

    The expression $k + k$ must be even. Adding any integer to itself doubles it, producing an even result, while $k + 2$, $k^2$, and $5k$ all stay odd when $k$ is odd.

91. What is the units digit of 7 raised to the fourth power?

    • A.1
    • B.3
    • C.7
    • D.9
    Show answerHide answer

    Correct answer: 1

    The units digit is 1. Powers of 7 cycle through units digits 7, 9, 3, 1, and the fourth power lands on 1.

92. If the product of two integers is odd, which of the following must be true?

    • A.One integer is zero
    • B.Both integers are even
    • C.Their sum is odd
    • D.Both integers are odd
    Show answerHide answer

    Correct answer: Both integers are odd

    Both integers must be odd. A product is odd only when every factor is odd; if either factor were even the product would be even.

93. When a positive integer is divided by 5, the remainder is 3. What is the remainder when that integer is multiplied by 3 and divided by 5?

    • A.1
    • B.2
    • C.4
    • D.3
    Show answerHide answer

    Correct answer: 4

    The remainder is 4. The integer equals $5q + 3$, so tripling gives $15q + 9$, and $9 \div 5$ leaves a remainder of 4.

94. What is $\frac{2}{3}$ plus $\frac{3}{4}$ written as a single fraction in lowest terms?

    • A.$\frac{5}{7}$
    • B.$\frac{5}{12}$
    • C.$\frac{11}{12}$
    • D.$\frac{17}{12}$
    Show answerHide answer

    Correct answer: $\frac{17}{12}$

    The sum is $\frac{17}{12}$. Using a common denominator of 12, $\frac{2}{3}$ is $\frac{8}{12}$ and $\frac{3}{4}$ is $\frac{9}{12}$; adding gives $\frac{17}{12}$, which is already in lowest terms.

95. What is 0.125 expressed as a fraction in lowest terms?

    • A.$\frac{1}{8}$
    • B.$\frac{1}{4}$
    • C.$\frac{1}{16}$
    • D.$\frac{125}{100}$
    Show answerHide answer

    Correct answer: $\frac{1}{8}$

    The fraction is $\frac{1}{8}$. Writing 0.125 as $\frac{125}{1000}$ and dividing numerator and denominator by 125 gives $\frac{1}{8}$.

96. What percent of 80 is 28?

    • A.28 percent
    • B.35 percent
    • C.30 percent
    • D.40 percent
    Show answerHide answer

    Correct answer: 35 percent

    The answer is 35 percent. Dividing 28 by 80 gives 0.35, which converts to 35 percent.

97. A shirt originally priced at 50 dollars is marked up by 20 percent. What is the new price?

    • A.60 dollars
    • B.55 dollars
    • C.62 dollars
    • D.70 dollars
    Show answerHide answer

    Correct answer: 60 dollars

    The new price is 60 dollars. A 20 percent markup adds $0.20 \cdot 50$, which is 10 dollars, giving $50 + 10 = 60$ dollars.

98. A store buys a lamp for 40 dollars and sells it at a 35 percent profit. What is the selling price?

    • A.52 dollars
    • B.56 dollars
    • C.58 dollars
    • D.54 dollars
    Show answerHide answer

    Correct answer: 54 dollars

    The selling price is 54 dollars. A 35 percent profit adds $0.35 \cdot 40$, which is 14 dollars, to the 40 dollar cost.

99. A sum of 1,500 dollars earns simple interest at 6 percent per year. How much interest accrues in 4 years?

    • A.240 dollars
    • B.300 dollars
    • C.360 dollars
    • D.420 dollars
    Show answerHide answer

    Correct answer: 360 dollars

    The interest is 360 dollars. Simple interest equals principal times rate times time: $1500 \cdot 0.06 \cdot 4 = 360$.

100. The ratio of pens to pencils in a drawer is 5 to 3. If there are 15 pens, how many pencils are there?

     • A.6
     • B.9
     • C.12
     • D.25
     Show answerHide answer

     Correct answer: 9

     There are 9 pencils. Each ratio unit equals $15 \div 5$, or 3 items, so the 3 units of pencils equal $3 \cdot 3 = 9$.

101. If 5 identical chairs cost 200 dollars, how much do 8 such chairs cost at the same rate?

     • A.280 dollars
     • B.320 dollars
     • C.300 dollars
     • D.360 dollars
     Show answerHide answer

     Correct answer: 320 dollars

     Eight chairs cost 320 dollars. The unit price is $200 \div 5$, which is 40 dollars per chair, and $8 \cdot 40 = 320$.

102. A prize of 120 dollars is split among three people in the ratio 3 to 4 to 5. How much does the person with the smallest share receive?

     • A.30 dollars
     • B.20 dollars
     • C.40 dollars
     • D.50 dollars
     Show answerHide answer

     Correct answer: 30 dollars

     The smallest share is 30 dollars. The ratio has $3 + 4 + 5 = 12$ units, so each unit equals $120 \div 12 = 10$ dollars, and the smallest share of 3 units is 30 dollars.

103. What is the value of 6 squared times 6?

     • A.6 to the second power
     • B.36
     • C.42
     • D.6 to the third power
     Show answerHide answer

     Correct answer: 6 to the third power

     The value is $6^3$. When multiplying powers of the same base, add the exponents, so $6^2 \cdot 6^1 = 6^3$.

104. What is the value of $\sqrt{169}$?

     • A.11
     • B.13
     • C.12
     • D.14
     Show answerHide answer

     Correct answer: 13

     The value is 13, because $13 \cdot 13 = 169$.

105. If 7x minus 4 equals 31, what is the value of x?

     • A.4
     • B.6
     • C.7
     • D.5
     Show answerHide answer

     Correct answer: 5

     The value of $x$ is 5. Adding 4 to both sides gives $7x = 35$, and dividing by 7 yields $x = 5$.

106. A subscription costs a 12 dollar setup fee plus 8 dollars per month. After how many months does the total reach 76 dollars?

     • A.6 months
     • B.7 months
     • C.8 months
     • D.9 months
     Show answerHide answer

     Correct answer: 8 months

     The total reaches 76 dollars after 8 months. Setting up $12 + 8m = 76$ and subtracting 12 gives $8m = 64$, so $m = 8$.

107. If 3x + 7 equals 5x minus 3, what is the value of x?

     • A.3
     • B.4
     • C.5
     • D.6
     Show answerHide answer

     Correct answer: 5

     The value of $x$ is 5. Subtracting $3x$ and adding 3 to both sides gives $10 = 2x$, so $x = 5$.

108. What are the solutions to x squared minus 7x + 10 equals 0?

     • A.X equals 2 or x equals 5
     • B.X equals 1 or x equals 10
     • C.X equals minus 2 or minus 5
     • D.X equals 5 or x equals 10
     Show answerHide answer

     Correct answer: X equals 2 or x equals 5

     The solutions are $x = 2$ or $x = 5$. The expression factors as $(x - 2)(x - 5)$, whose roots add to 7 and multiply to 10.

109. If x squared equals 64, what are the possible values of x?

     • A.8 only
     • B.Minus 8 only
     • C.8 or minus 8
     • D.0 or 8
     Show answerHide answer

     Correct answer: 8 or minus 8

     The values are 8 or $-8$. Both $8^2$ and $(-8)^2$ equal 64.

110. Which of the following describes the solution to 4x + 5 is greater than or equal to 17?

     • A.X is greater than or equal to 3
     • B.X is less than or equal to 3
     • C.X is less than or equal to 12
     • D.X is greater than or equal to 12
     Show answerHide answer

     Correct answer: X is greater than or equal to 3

     The solution is $x \ge 3$. Subtracting 5 gives $4x \ge 12$, and dividing by the positive 4 keeps the direction, yielding $x \ge 3$.

111. What is the value of the absolute value of (negative 12) plus the absolute value of (negative 5)?

     • A.7
     • B.Minus 7
     • C.Minus 17
     • D.17
     Show answerHide answer

     Correct answer: 17

     The value is 17. The absolute value of $-12$ is 12 and of $-5$ is 5, and adding these nonnegative distances gives 17.

112. Simplify the expression 5(x + 1) minus 2(x minus 3).

     • A.3x + 11
     • B.3x minus 1
     • C.7x + 11
     • D.3x + 1
     Show answerHide answer

     Correct answer: 3x + 11

     The simplified form is $3x + 11$. Distributing gives $5x + 5 - 2x + 6$, and combining like terms produces $3x + 11$.

113. Which of the following is the expanded form of (x + 6) squared?

     • A.X squared plus 36
     • B.X squared plus 6x plus 36
     • C.X squared plus 12x plus 36
     • D.X squared plus 12x plus 12
     Show answerHide answer

     Correct answer: X squared plus 12x plus 36

     The expansion is $x^2 + 12x + 36$. Squaring a binomial gives the first term squared, twice the product of the terms, and the last term squared, so the middle term is $2 \cdot 6 \cdot x = 12x$.

114. Which expression is equivalent to (8x squared minus 12x) divided by 4x, for x not equal to 0?

     • A.2x minus 3
     • B.2x squared minus 3
     • C.2x minus 12
     • D.4x minus 3
     Show answerHide answer

     Correct answer: 2x minus 3

     The simplified expression is $2x - 3$. Dividing each term by $4x$ gives $8x^2 \div 4x = 2x$ and $12x \div 4x = 3$, so the result is $2x - 3$.

115. If f(x) equals x squared minus 2x + 1, what is the value of f(4)?

     • A.7
     • B.11
     • C.13
     • D.9
     Show answerHide answer

     Correct answer: 9

     The value is 9. Substituting 4 for $x$ gives $16 - 8 + 1$, which equals 9.

116. If f(x) equals 2x minus 3 and g(x) equals x + 5, what is the value of g(f(4))?

     • A.8
     • B.10
     • C.14
     • D.12
     Show answerHide answer

     Correct answer: 10

     The value is 10. First $f(4) = 2 \cdot 4 - 3 = 5$, then $g(5) = 5 + 5 = 10$.

117. A copier makes 80 copies in 5 minutes. How many minutes does it take to make 400 copies at the same rate?

     • A.20 minutes
     • B.30 minutes
     • C.32 minutes
     • D.25 minutes
     Show answerHide answer

     Correct answer: 25 minutes

     It takes 25 minutes. The rate is $80 \div 5 = 16$ copies per minute, and $400 \div 16 = 25$ minutes.

118. A swimmer covers 1,200 meters in 30 minutes. What is the swimmer's speed in meters per minute?

     • A.30 meters per minute
     • B.36 meters per minute
     • C.40 meters per minute
     • D.45 meters per minute
     Show answerHide answer

     Correct answer: 40 meters per minute

     The speed is 40 meters per minute. Dividing 1,200 meters by 30 minutes gives 40 meters per minute.

119. If $n$ is a positive integer, which of the following expressions always represents an odd number?

     • A.$2n$
     • B.$n + n$
     • C.$2n + 1$
     • D.$4n$
     Show answerHide answer

     Correct answer: $2n + 1$

     The expression $2n + 1$ is always odd. Twice any integer is even, and adding 1 to an even number produces an odd result; the other choices are all even.

120. What is the smallest prime number greater than 50?

     • A.51
     • B.53
     • C.55
     • D.57
     Show answerHide answer

     Correct answer: 53

     The smallest prime greater than 50 is 53. The value 51 equals $3 \cdot 17$, 55 equals $5 \cdot 11$, and 57 equals $3 \cdot 19$, so each is composite, while 53 has no divisors other than 1 and itself.

121. The units digit of 7 raised to a positive integer power repeats in a cycle of which length?

     • A.2
     • B.3
     • C.4
     • D.1
     Show answerHide answer

     Correct answer: 4

     The units digit of powers of 7 repeats in a cycle of length 4, following the pattern 7, 9, 3, 1 before repeating, so the cycle length is 4.

122. When a positive integer is divided by 5, the remainder is 3. What is the remainder when three times that integer is divided by 5?

     • A.4
     • B.3
     • C.1
     • D.2
     Show answerHide answer

     Correct answer: 4

     The remainder is 4. Multiplying the integer by 3 gives a remainder of 9 when divided by 5, and $9 - 5$ leaves 4.

123. What is the greatest common divisor of 84 and 126?

     • A.14
     • B.42
     • C.21
     • D.28
     Show answerHide answer

     Correct answer: 42

     The greatest common divisor is 42. Since 84 equals $2^2 \cdot 3 \cdot 7$ and 126 equals $2 \cdot 3^2 \cdot 7$, the shared factors are 2, 3, and 7, whose product is 42.

124. What is $\frac{2}{5}$ plus $\frac{1}{3}$ written as a single fraction in lowest terms?

     • A.$\frac{3}{8}$
     • B.$\frac{11}{15}$
     • C.$\frac{3}{15}$
     • D.$\frac{2}{15}$
     Show answerHide answer

     Correct answer: $\frac{11}{15}$

     The sum is $\frac{11}{15}$. Using a common denominator of 15, $\frac{2}{5}$ becomes $\frac{6}{15}$ and $\frac{1}{3}$ becomes $\frac{5}{15}$, and adding gives $\frac{11}{15}$, which cannot be reduced.

125. What is 0.24 expressed as a fraction in lowest terms?

     • A.$\frac{6}{25}$
     • B.$\frac{24}{100}$
     • C.$\frac{12}{25}$
     • D.$\frac{1}{4}$
     Show answerHide answer

     Correct answer: $\frac{6}{25}$

     The value equals $\frac{6}{25}$. Writing 0.24 as $\frac{24}{100}$ and dividing numerator and denominator by their common factor of 4 gives $\frac{6}{25}$.

126. A television priced at 450 dollars is discounted by 20 percent. What is the sale price?

     • A.340 dollars
     • B.350 dollars
     • C.360 dollars
     • D.380 dollars
     Show answerHide answer

     Correct answer: 360 dollars

     The sale price is 360 dollars. A 20 percent discount removes $0.20 \cdot 450$, which is 90 dollars, leaving $450 - 90$, or 360 dollars.

127. A quantity decreases from 250 to 200. What is the percent decrease?

     • A.20 percent
     • B.25 percent
     • C.15 percent
     • D.50 percent
     Show answerHide answer

     Correct answer: 20 percent

     The decrease is 20 percent. The change of 50 is divided by the original 250, giving 0.20, or 20 percent.

128. A principal of 6,000 dollars earns simple interest at 4 percent per year. How much interest accrues in 5 years?

     • A.1,000 dollars
     • B.1,200 dollars
     • C.1,500 dollars
     • D.2,400 dollars
     Show answerHide answer

     Correct answer: 1,200 dollars

     The interest is 1,200 dollars. Simple interest equals principal times rate times time, so $6000 \cdot 0.04 \cdot 5$ equals 1,200 dollars.

129. The ratio of teachers to students at a school is 2 to 25. If there are 16 teachers, how many students are there?

     • A.180
     • B.200
     • C.225
     • D.150
     Show answerHide answer

     Correct answer: 200

     There are 200 students. Each ratio unit equals $16 \div 2$, which is 8, so the 25 units of students equal $25 \cdot 8$, or 200.

130. If 9 identical tickets cost 36 dollars, how much do 13 such tickets cost at the same rate?

     • A.48 dollars
     • B.50 dollars
     • C.52 dollars
     • D.56 dollars
     Show answerHide answer

     Correct answer: 52 dollars

     They cost 52 dollars. Each ticket costs $36 \div 9$, which is 4 dollars, and $13 \cdot 4$ equals 52 dollars.

131. What is the value of $6^2$ minus $\sqrt{49}$?

     • A.29
     • B.31
     • C.36
     • D.43
     Show answerHide answer

     Correct answer: 29

     The value is 29. Six squared equals 36 and $\sqrt{49}$ equals 7, so $36 - 7$ equals 29.

132. If $7x + 5$ equals $3x + 29$, what is the value of $x$?

     • A.4
     • B.5
     • C.7
     • D.6
     Show answerHide answer

     Correct answer: 6

     The value of $x$ is 6. Subtracting $3x$ and 5 from both sides gives $4x$ equals 24, and dividing by 4 yields $x$ equals 6.

133. For which values of $x$ is the statement $6x - 5 \ge 2x + 7$ true?

     • A.$x \le 3$
     • B.$x \ge 3$
     • C.$x \le 12$
     • D.$x \ge 12$
     Show answerHide answer

     Correct answer: $x \ge 3$

     The solution is $x \ge 3$. Subtracting $2x$ and adding 5 gives $4x \ge 12$, and dividing by the positive 4 keeps the direction, yielding $x \ge 3$.