Review Contents

Problem Solving

1. The probability that it will rain in NYC on any given day in July is 30%. what is the probability that it will rain on exactly 3 days from July 5 to July 10 ? (October 23, 2001)
   Ans: 6! / (6 - 3)!3! x 0.3 x 0.3 x 0.3 x 0.7 x 0.7 x 0.7
    
2. The inlet pipe can fill the empty swimming pool in 8 hours, while the outlet pipe can empty the pool from full capacity in 12 hours. if both pipes are opened when the tank is 25% full, how many hours from there does it take for the tank to fill to 90% capacity ? (October 23, 2001)
   Ans: 15.6 hrs.
    
3. How many different signals can be transmitted by hoisting 3 red, 4 yellow and 2 blue flags on a pole, assuming that in transmitting a signal all nine flags are to be used? (October 05, 2001)
   Ans: 9! / 3!4!2!
    
4. which of the following is an integer ?

I. (12!8!) / (6!9!)
II. (15!8!) / (5!3!9!)
III (8!8!) / (16!)
Ans: I and II

5. Code words can be generated in a sequence of following 10 letters A, B, C, D, E, F, G, H, I, J. What's the ratio of number of 5 letter code words to number of 4 letter code words?(September 30, 2001)
   Ans:   A.4:3   B.3:2   C. 4:1  D. 5:1   E. 6:1
    
6. If John was on a camping trip (starting on Saturday) and would leave if it rained. Would he go home on Monday? There's a 20% chance of raining each day. (September 30, 2001)
   Ans: 12.8%
    
7. John can paint a room in 5 hours, while Jack can paint the  same room in 6 hours. At 8:00am, both start painting  the room together. At 9:30am, Pete arrives and helps out. Pete can paint  the room by himself in 12 hours. At what time  will the 3 of them finish painting the room? (September 10, 2001)
   Ans: 10:30 am
    
8. A parking lot has N autos. There are one fourth as many cars as there are trucks. 3/5 of the trucks are pickups.
   In terms of N, how many of the autos are pickups? (September 3, 2001)
   Ans: 12N/25 (Some say 9N/20, if so your explanation is really appreciated.)
    
9. There are 9 books on a shelf, 7 hard cover and 2 soft cover. How many different combinations exist in which you choose 4 books from the 9 and have at least one of them be a soft cover book? (September 3, 2001)
   Ans: 91

Data Sufficiency

1. What is the thousands digit of 640 to the n^th power if n is an integer ? (September 10, 2001)
   1. n < 6
   2. n > 4
   
   Ans: B
    
2. p, q, r are integers. Is the product pqr odd ? (September 10, 2001)
   1. the product pr is odd.
   2. the product pq is odd.
   Ans: C