Now that you’ve learned some of the strategies for the Word Problem section of the SSAT, test your knowledge with some practice questions!
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).
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.
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.
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).
B: Let the number be x. Translating gives you 3 + 4x = 11. Therefore, 4x = 8 and x = 2.
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
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