A club had 3 boys and 5 girls. During a membership drive the same number of boys and girls joined the club. How many members does the club have now if the ratio of boys to girls is 3:4?
A. 12
B. 14
C. 16
D. 21
E. 28
Solution Suppose that x boys and x girls joined the club. Then, the new ratio of boys to girls would be (3 + x) :( 5 + x), which you are told is 3:4, and 3+x/5+x =3/4 ⇒ 4(3 + x) = 3(5 + x) ⇒12 + 4x = 15 + 3x x = 3. Therefore, 3 boys and 3 girls joined the existing 3 boys and 5 girls, for a total of 14 members. The correct answer is B.
If 15 workers can paint a certain number of houses in 24 days, how many days will 40 workers take, working at the same rate, to do the same job?
A. 15
B. 12
C. 10
D. 9
E. 7
Solution Clearly, the more workers there are, the less time will be required, so used multiplication. The jib takes: (15 workers) × (24 days) = 360 worker-days. Then (40 workers) × (d days) = 360 worker-days. 40x = 360 d = 9 days. This can also be set up as follows:360 worker-days/ 40workers = 9 days.
A hospital has enough pills on hand to tread 10 patients for 14 days. How long will the pills last if there are 35 patients?
A. 8
B. 6
C. 5
D. 4
E. 3
Solution We are told that has enough pills to last for 10 × 14 = 140 patient-days: 140 patient-days = (10 patients) × (14 days). 140 patient-days = (20 patients) × (7 days). 140 patient-days = (70 patients) × (2 days). To solve this question, write: 140 patient-days = (35 patients) × (d days) ⇒d = 140/35 = 4.
Sharon read 24 pages of her book in 15 minute. At this rate, how many pages can she read in 40 minute?
A. 70
B. 66
C. 65
D. 64
E. 62
Solution Handle the rate of the problem exactly like a ratio problem. Set up a proportion and cross-multiply: pages/ minutes=24/15 = x/40 ⇒15x = 40 × 24 = 960 ⇒x = 64.
Wendy drew a square. She then erased it and drew a second square whose sides were 3 times the sides of the first square. By what percent was the area of the square increased?
A. 900%
B. 850%
C. 800%
D. 700%
E. 600%
Solution Assume that the sides of the first square were 1 inch long, so that the area was 1 square inch. Then, the sides of the second square were 3 inch long, and it area was 9 square inches, an increase of 8 square inches or 800%.
