July 21st, 2007[quantitative]

1. Point Q lies at the center of the square base (ABCD) of the pyramid pictured above. The pyramid’s height (PQ) measures exactly one half the length of each edge of its base, and point E lies exactly halfway between C and D along one edge of the base. What is the ratio of the surface area of any of the pyramid’s four triangular faces to the surface area of the shaded triangle?

1. 3 :√2
2. √5:1
3. 4√3:3
4. 2√2:1
5. 8:√5

2. 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

3. 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

4. A portion of $7200 is invested at a 4% annual return, while the remainder is invested at a 5% annual return. If the annual income from both portions is the same, what is the total income from the two investments?

1. $160
2. $320
3. $400
4. $720
5. $1,600

5. (1/4)³ + (3/4)³ + 3(1/4)(3/4)(1/4 + 3/4) =?

1. 1/64
2. 27/64
3. 49/64
4. 0
5. 1

http://www.file27.com/id827/Quant15.txt