This is the first in our series of free SAT Math practice tests. It is based on the fourth section of the SAT, in which you are allowed to use a calculator. The SAT Math test went through a major revision in 2016, changing the focus to real world problems. Questions now include problems you might encounter at work, in your daily life, or in your college math and science courses. Try our SAT Math multiple choice questions to see if you are fully prepared for this section of the test.

**Directions:** Solve each problem and select the best of the answer choices provided. The use of a calculator is permitted.

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Question 1 |

**There are 5 pencil-cases on the desk. Each pencil-case contains at least 10 pencils, but not more than 14 pencils. Which of the following could be the total number of pencils in all five pencil-cases?**

35 | |

45 | |

65 | |

75 |

If all pencil-cases have 10 pencils (the minimum number of pencils every pencil-case can hold), then the total minimum number of pencils is 10 × 5 = 50 pencils.

Likewise, if all pencil-cases have 14 pencils (the maximum number of pencils every pencil-case can hold), then the total maximum number of pencils is 14 × 5 = 70 pencils.

Thus, the answer must be between 50 and 70. Out of all the possible answer choices, only (C), 65 pencils, matches these criteria.

Question 2 |

**A bag contains 3 black marbles, 6 red marbles and 9 white marbles. If you randomly select a marble from the bag, what is the probability of getting a red marble?**

$\dfrac{1}{7}$ | |

$\dfrac{6}{12}$ | |

$\dfrac{1}{2}$ | |

$\dfrac{1}{3}$ |

The probability of getting a red marble is:

$\dfrac{Number~of~red~marbles}{Total~number~of~marbles}$

The total number of red marbles: 6

The total number of marbles: 3 + 6 + 9 = 18.

Simplify:

$\dfrac{6}{18} = \dfrac{1}{3}$

Question 3 |

**A bird traveled 72 miles in 6 hours flying at constant speed. At this rate, how many miles did the bird travel in 5 hours?**

12 | |

30 | |

60 | |

14.4 |

First calculate the rate that the bird is traveling at:

$\frac{72~miles}{6~hour} = 12~miles~per~hour$

The distance traveled in 5 hours will be:

$12~miles~per~hour * 5~hours = 60~miles$

Question 4 |

**Three kids own a total of 96 comic books. If one of the kids owns 16 of the comic books, what is the average (arithmetic mean) number of comic books owned by the other two kids?**

40 | |

42 | |

44 | |

46 |

If one kid owns 16 of the comic books, then the number of comic books owned by the other two kids is: 96 − 16 = 80.

Therefore, the average is: 80 ÷ 2 = 40.

Question 5 |

**If David has twice as many nickels as Tom, and Tom has 15 more nickels than John, how many dollars does David have if John has 6 nickels?**

2.1 | |

21 | |

42 | |

14 |

If John has 6 nickels, then Tom has 15 + 6 = 21 nickels.

If David has twice as many nickels as Tom, then David has 21 × 2 = 42 nickels.

A nickel is worth 5 cents, so 42 nickels will be worth 42 × 5 = 210 cents. Because every dollar is worth 100 cents, this is equivalent to:

$\dfrac{210}{100}$ = 2.1 dollars.

Question 6 |

**The total cost of 4 equally priced pens is $6. If the cost per pen is increased by 25 cents, how much will 3 of these pens cost at the new rate?**

$5.25 | |

$5.00 | |

$5.50 | |

$8.25 |

First, figure out the cost per pen:

Cost = 6 ÷ 4 = 1.5

Next, figure out the cost per pen after the 0.25 price increase:

Cost = 1.5 + 0.25 = 1.75

Thus, the cost of 3 pens will be 3 × 1.75 = $5.25

Question 7 |

**A “Triangle” is any positive integer greater than 1 that has only three positive integer factors: itself, its square root, and 1. Which of the following is a Triangle?**

169 | |

100 | |

36 | |

81 |

The only factors of 169 are: 169, 13, and 1. (The square root of 169 is 13.) All of the other options have more than 3 factors.

Question 8 |

**The sum of two positive integers is 13. The difference between these numbers is 7. What is their product?**

12 | |

22 | |

30 | |

40 |

Use the given information to create a system of equations in two variables and then solve with the method of combination. Translating the problem statement into algebra:

x + y = 13

x − y = 7

Add the 2 equations together:

x + x = 13 + 7;

Now solve for x:

2x = 20; x = 10

The value of y can then be found. Once the variable values are found, their product can be computed:

x * y = 10 * 3 = 30

Question 9 |

**What is the difference between the median and the mode in the following set of data?**72, 44, 58, 32, 34, 68, 94, 22, 67, 45, 58

0 | |

2 | |

4 | |

6 |

Start by organizing the data numerically from least to greatest: 22, 32, 34, 44, 45, 58, 58, 67, 68, 72, 94

The mode, or data value that occurs most often, is 58.

The median, or data value in the middle of the data set, is also 58.

The difference between these values is 0.

Question 10 |

**The table above, which describes the New York City workforce, is only partially filled. Based on this information, how many women in the New York City workforce are unemployed?**

500 | |

1,500 | |

2,500 | |

3,500 |

First, we can compute the number of employed women by using the numbers in the first column:

40,000 − 22,000 = 18,000

Then, we can compute the number of unemployed women by using the data in the second row:

21,500 − 18,000 = 3,500

Thus, 3,500 women in the New York City workforce are unemployed.

List |

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