Problem Solving MCQ Set 4

Question: An empty swimming pool can be filled to capacity through an inlet pipe in 3 hours, and it can be completely drained by a drainpipe in 6 hours. If both pipes are fully open at the same time, in how many hours will the empty pool be filled to capacity?

1. 4
2. 4.5
3. 5
4. 5.5
5. 6

Question: If r = (3p + q)/2 and s = p - q, for which of the following values of p would r2 = s2?

1. 1q/5
2. 10 - 3q/2
3. q - 1
4. 3q
5. 9q/2 - 9

Question: At 10 a.m. two trains started traveling toward each other from stations 287 miles apart. They passed each other at 1:30 p.m. the same day. If the average speed of the faster train exceeded the average speed of the slower train by 6 miles per hour, which of the following represents the speed of the faster train, in miles per hour?

1. 38
2. 40
3. 44
4. 48
5. 50

Question: On the xy-coordinate plane, points A and B both lie on the circumference of a circle whose center is O, and the length of AB equals the circle's diameter. If the (x,y) coordinates of O are (2,1) and the (x,y) coordinates of B are (4,6), what are the (x,y) coordinates of A?

1. (3, 3/2)
2. (1, 2/2)
3. (0, -4)
4. (2/2, 1)
5. (-1, -2/2)

Question: If a rectangle's length and width are both doubled, by what percent is the rectangle's area increased?

1. 50
2. 100
3. 200
4. 300
5. 400

Question: A rectangular tank 10" by 8" by 4" is filled with water. If all of the water is to be transferred to cube-shaped tanks, each one 3 inches on a side, how many of these smaller tanks are needed?

1. 9
2. 12
3. 16
4. 21
5. 39