1. The product of which of the following pairs of numbers is closest to 5,678?
A. 5 and 990
B. 6 and 900
C. 6 and 950 Correct
D. 7 and 800
E. 7 and 850
Explanation
Step 1: Multiply each pair. 5 * 990 = 4,950; 6 * 900 = 5,400; 6 * 950 = 5,700; 7 * 800 = 5,600; 7 * 850 = 5,950. Step 2: Compare differences from 5,678. The differences are 728, 278, 22, 78, and 272. Step 3: The smallest difference is 22, so 6 * 950 = 5,700 is closest.
2. Chairs are to be arranged in a school gymnasium so that the number of chairs in each row will be 8 greater than the number of rows. If a total of 660 chairs are to be arranged in this fashion, how many rows of chairs will there be?
A. 12
B. 22 Correct
C. 26
D. 30
E. 55
Explanation
Let the number of rows be r. Then each row has (r + 8) chairs, and the total number of chairs is r × (r + 8) = 660. This gives the quadratic equation r² + 8r ? 660 = 0. Solving using the quadratic formula: r = [-8 ± ?(64 + 2640)] / 2 = [-8 ± ?2704] / 2 = [-8 ± 52] / 2. The positive solution is (-8 + 52)/2 = 44/2 = 22. Thus, there are 22 rows (and each row has 30 chairs, since 22 × 30 = 660). The number of rows is 22.
3. The list shown gives the number of movies that each of six of Sam's friends saw last year: 12, 17, 9, 11, 12, 14. Sam's sister Lucy saw 7 fewer movies last year than Sam did. The range of the numbers of movies that Sam, Lucy, and each of the six friends saw last year was 10. Which of the following could be the number of movies that Sam saw last year?
A. 14 Correct
B. 15
C. 16
D. 17
E. 18
Explanation
The six friends saw 9, 11, 12, 12, 14, and 17 movies last year, so the current range among them is 17 – 9 = 8. When Sam (S movies) and Lucy (S – 7 movies) are added, the overall range of all eight numbers must become exactly 10. The only way to increase the range from 8 to exactly 10 is if Lucy becomes the new minimum: 17 – (S – 7) = 10 ? S – 7 = 7 ? S = 14. Then Lucy saw 7 movies, and the full list is 7, 9, 11, 12, 12, 14, 14, 17, giving a range of 17 – 7 = 10. No other value of S in the options produces a range of exactly 10, so Sam saw 14 movies last year.
4. Amin's salary was decreased by 20% in 2015, but he got an increase of 50% in 2016. Suri's salary was increased by 50% in 2015 and again by 6.67% in 2016. If Amin's salary was 10% less than Suri's salary in 2016, by what percent was Amin's salary more or less than Suri's salary in 2014?
A. 20% less
C. 10% more
D. 20% more Correct
E. 25% more
Explanation
Let Suri’s salary in 2014 be 100. After a 50% increase in 2015, Suri earns 150, and after a 6.67% (1/15) increase in 2016, Suri earns 150 × 16/15 = 160. Since Amin’s salary in 2016 is 10% less than Suri’s, Amin earns 160 × 0.9 = 144 in 2016. Working backwards, Amin’s 2015 salary (before his 50% increase) was 144 ÷ 1.5 = 96, and his 2014 salary (before the 20% decrease) was 96 ÷ 0.8 = 120. Therefore, in 2014 Amin earned 120 while Suri earned 100, meaning Amin’s salary was 20% more than Suri’s in 2014.
5. Two weeks ago a certain sweater was offered at a sale price that was 20 percent less than the retail price, and last week it was offered at a clearance price that was 30 percent less than the sale price. The clearance price of the sweater was what percent less than the retail price?
A. 40%
B. 44% Correct
C. 50%
D. 56%
E. 0.6
Explanation
Let retail = 100. Sale price = 100 * 0.8 = 80. Clearance = 80 * 0.7 = 56. Discount from retail: (100 - 56)/100 = 44% less.