ssat-word-problems-practice-questions

SSAT Word Problem Practice Questions

Now that you’ve learned some of the strategies for the Word Problem section of the SSAT, test your knowledge with some practice questions!

Question 1

The original price of a television decreases by 20 percent. By what percent must the discounted price increase to reach its original value?

(A) 15%

(B) 20%

(C) 25%

(D) 30%

(E) 40%

Answer 1

C: It is important to note that while the value of the television decreases and increases by the same dollar amount, it doesn’t increase and decrease by the same percent. Let’s pick $100 for the price of the television. If the price decreases by 20%, and since 20% of $100 is $20, the price decreases by $20. The new price is $100 − $20, or $80. For the new price to reach the original price ($100), it must be increased by $20. Twenty dollars is 1 4 of 80, or 25% of $80. The new price must be increased by 25%, choice (C).

Question 2

A worker earns $15 an hour for the first 40 hours he works each week and one and a half times this much for every hour over 40 hours. If he earned $667.50 for one week’s work, how many hours did he work?

(A) 40

(B) 41

(C) 42

(D) 43

(E) 44

Answer 2

D: Run the answer choices through the information in the stem to see which one gives a total of $667.50. Since the answer choices are in numerical order, start with the middle choice, (C). If he works for 42 hours, he earns $15 per hour for the first 40 hours, or $600, and he earns 1 1 2 times his normal rate for the two extra hours. So 3/2 times $15 is $22.50 per hour, and since he worked 2 hours at that rate, he made an additional $45. The total is $645, which isn’t enough. So (C) is too small, as are (A) and (B). Now try (D). He still earns $600 for the first 40 hours, but now you have to multiply the overtime rate, $22.50, by 3, which gives you $67.50. The total is $667.50, which means that (D) is correct. Another way to approach the question is to see that for the first 40 hours, the worker earns $15 an hour: 40 hours × $15 an hour = $600. For any additional hours, he earns one and a half times $15. So 1.5 × $15 = $22.50 per hour. If he earned $667.50 in one week, $600 was earned in the first 40 hours and the remaining $67.50 was earned working additional hours. To find out how many additional hours the worker worked, divide the amount earned ($67.50) by the amount earned per hour ($22.50). And $67.50 ÷ $22.50 = 3. So 40 hours + 3 additional hours equals 43 hours.

Question 3

Liza has 40 less than three times the number of books that Janice has. If B is equal to the number of books that Janice has, which of the following expressions shows the total number of books that Liza and Janice have together?

(A) 3B − 40

(B) 3B + 40

(C) 4B − 40

(D) 4B

(E) 4B + 40

Answer 3

C: This is a straightforward translation problem. You’re told that Janice has B books. Liza has 40 less than three times the number of books Janice has, which you can translate as L = 3B − 40. The total number they have together equals B + (3B − 40), or 4B − 40.

Question 4

Yesterday, a store sold 8 times as many hats as it sold coats. It also sold 3 times as many sweaters as it sold coats. What could be the total number of hats, sweaters, and coats that were sold?

(A) 16

(B) 21

(C) 25

(D) 36

(E) 54

Answer 4

D: Let x be the number of coats that the store sold yesterday. Keep in mind that x must be an integer. The store sold 8 times the number of hats as coats yesterday. So the store sold 8x hats. The store sold 3 times the number of sweaters as coats yesterday. So the store sold 3x sweaters. The total number of hats, sweaters, and coats that the store sold was 8x + 3x + x = 12x. Since x is an integer, 12x must be a multiple of 12. Only (D), 36, is a multiple of 12 (36 = 3 × 12).

Question 5

If 3 added to 4 times a number is 11, the number must be

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Answer 5

B: Let the number be x. Translating gives you 3 + 4x = 11. Therefore, 4x = 8 and x = 2.

Question 6

Liz worked 3 hours less than twice as many hours as Rachel did. If W is the number of hours Rachel worked, which of the following expressions shows the total number of hours worked by Liz and Rachel together?

(A) 2W − 3

(B) 2W + 3

(C) 3W − 3

(D) 3W + 3

(E) 4W − 2

Answer 6

C: Rachel worked W hours, and Liz worked 3 hours less than twice as many hours as Rachel, or 2W − 3. Add these expressions to find the total number of hours worked by Liz and Rachel together: W + 2W − 3 = 3W − 3

Question 7

Five less than 3 times a certain number is equal to twice the original number plus 7. What is the original number?

(A) 2

(B) 2 2/5

(C) 6

(D) 11

(E) 12

Answer 7

E: Call the unknown number x. Five less than 3 times the number, or 3x − 5, equals twice the original number plus 7, or 2x + 7. So 3x − 5 = 2x + 7. Solve for x:

3x − 5 = 2x + 7

x − 5 = 7

x = 12

Need some help prepping for the SSAT? Check out Kaplan’s study resources!