Start you math prep with our free SAT Math practice test. There are four major content areas covered on the SAT Math test: 1) Numbers & operations. 2) Algebra & functions 3) Geometry & measurement 4) Data analysis, statistics, & probability.

**Directions:** Solve each problem and select the best of the answer choices given.

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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?

25 | |

35 | |

45 | |

65 | |

75 |

Question 1 Explanation:

If all pencil-cases have 14 pencils (the maximum number of pencil every pencil-case can hold), then they can hold a total of 14 x 5 = 70 pencils. By doing such, we can eliminate answer (E) 75 pencils. The least amount of pencils these five pencil-cases would hold is 10 x 5= 50. We can eliminate (A), (B) and (C) because these answers are less than 50. We are then left with (D). 65.

Question 2 |

If x is 6 less than y and y is twice of z, then what is the value of x when z=2?

10 | |

8 | |

-2 | |

12 | |

-5 |

Question 2 Explanation:

We know y is twice of z, so y should be 2 x 2 =4. If y= 4 and x is 6 less than y, 4 – 6 = -2. X is equal to -2, answer (C) is correct.

Question 3 |

“All multiples of 7 are odd.”
Which of the following numbers provides a counterexample to this statement?

7 | |

12 | |

21 | |

84 | |

49 |

Question 3 Explanation:

Counterexample is an exception to the rule. (D). 84 is a multiple of 7 (7 x 12 = 84), but it is not an odd number.

Question 4 |

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 | |

30 |

Question 4 Explanation:

If John has 6 nickels, then Tom has 15 + 6 = 21 nickels. Since the number of nickels David has is twice the nickels Tom has, then 21 x 2 = 42. A nickel is worth 5 cents, so 42 nickels will be worth 42 x 5 = 210 cents which is equivalent to 210 ÷ 100 (Every dollar worth 100 cents) = 2.1 dollars.

Question 5 |

4x4-4+4x4 =?

64 | |

28 | |

-4 | |

4 | |

-16 |

Question 5 Explanation:

The Order of Operation Rule says do multiplication/division first and then do addition/subtraction. Hence, the first part of multiplication: 4 x 4 =16. The second multiplication: 4 x 4 =16. Then subtract 4 from the first 16 (16 – 4 = 12), and then add the second 16, which come out to be 12 + 16 = 28, (B).

Question 6 |

If x+3 = y, then 2x+6 =?

y | |

4y | |

3y | |

2y | |

cannot be determined |

Question 6 Explanation:

We can also rewrite 2x + 6 as 2(x +3) because when you distribute 2(x +3), it comes out to be 2x + 6. So the answer of the expression of 2x + 6 should be 2 times the answer of x+3. If x+3 = y, then 2(x+3) = 2y. The correct answer is (D).

Question 7 |

Lisa received a $100 gift card for her birthday. She bought a pair of $30 new sneakers, a $23 dress and two $17 SAT books, how much money does she have left on the card?

13 | |

30 | |

70 | |

87 | |

45 |

Question 7 Explanation:

The total amount of money Amy spent is 30 + 23 + 2 x 17 (because she brought 2 SAT books and they are $17 each) = 87. And then subtract the amount she spend from the total amount, Amy still has 100 – 87 = 13 dollars left on the gift card. The answer is (A).

Question 8 |

For their school uniform, each student can choose from 4 types of tops and 3 types of bottoms. How many combinations of tops and bottoms are there?

7 | |

12 | |

1 | |

10 | |

24 |

Question 8 Explanation:

For every top the students choose, there are 3 options for bottom. If there are 2 tops students can choose from, and 3 options for the bottom, students will have total of 6 combinations, 2 x 3= 6. Because for a different top, even if the students choose the same bottom, they are still two different combinations. Hence just multiply the number of the option for tops and bottoms; the total number of combinations is 4 x 3 = 12, (B).

Question 9 |

3(x-4)=18, what is the value of x?

14/3 | |

22/3 | |

6 | |

10 | |

22 |

Question 9 Explanation:

First, distribute 3. We get 3x – 3 x 4 = 18 which is same as 3x – 12 = 18. Next, isolate 3x by adding 12 on both sides: 3x = 18 + 12. Finally, Divide both side by 3 to find the value of x: 3x/3 = 30/3, x = 10. The correct answer is (D).

Question 10 |

A bag contains 3 black marbles, 6 red marbles and 9 white marbles. What is the probability of getting a red marble?

1/7 | |

6/12 | |

1/2 | |

1/3 | |

50% |

Question 10 Explanation:

The probability of getting a red marble is: the number of red marbles out of the total number of marbles in the bag. The total number of marbles is: 3 + 6 + 9 =18. Then, simplify 6/18 to 1/3. The answer is (D).

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