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Answers to Sample Questions

CIS Scholarship Exam

Question 1

Suppose that at a certain manufacturing plant, process X can be done in either of two ways: by doing process A ten times or by doing process D once followed by process E twenty times. Process A consists of doing process B five times followed by process C once. Process B takes four seconds, process C takes six seconds, process D takes eleven seconds, and process E takes twelve seconds. What is the largest amount of time that it could take to do process X?

a) 200 seconds

b) 251 seconds

c) 260 seconds

d) 511 seconds

e) None of the above.

Answer

If process A is chosen, then the amount of time is 10 * [5(4) + 6] = 260. If not, then the amount of time is 11 + 20(12) = 251. Clearly, the 260 seconds is the largest. The answer is c.

Question 2

In a certain game, player A starts out with $65, player B with $100, and player C with $180. The rules of the game are as follows:

Play begins with player A, then proceeds to player B, then to player C, back to A, etc.

When it is a player's turn, each player is automatically given $10. If the player whose turn it is has more money than each of the other players, this player gives $20 to each of the other players. This can mean that this player might have to borrow money from the bank, thus ending up with a negative balance.

Play continues until on a given turn the player achieves a balance of $250 or more. This player is the winner. A check is made to see if there is a winner at two places: after paying each player the $10, and again after giving $20 to the two other players (if this is done at all).

Question: Who wins in the game having the starting amounts indicated above?

a) Player A

b) Player B

c) Player C

d) Players A and C are tied for the winning position.

e) None of the above.

Answer

Here is a trace that shows each step of the game. Read the game's directions carefully as a minor misinterpretation can change the outcome. The answer is c.

Current amounts for A, B, C: 65 100 180
Current amounts for A, B, C: 75 110 190
Current amounts for A, B, C: 85 120 200
Current amounts for A, B, C: 95 130 210
Current amounts for A, B, C: 115 150 170
Current amounts for A, B, C: 125 160 180
Current amounts for A, B, C: 135 170 190
Current amounts for A, B, C: 145 180 200
Current amounts for A, B, C: 165 200 160
Current amounts for A, B, C: 175 210 170
Current amounts for A, B, C: 185 220 180
Current amounts for A, B, C: 205 180 200
Current amounts for A, B, C: 215 190 210
Current amounts for A, B, C: 225 200 220
Current amounts for A, B, C: 185 220 240
Current amounts for A, B, C: 195 230 250
Player C is a winner with a total of 250


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