Civil Service Commission Past Questions and Answers


16)

In an office there was a small cash box. One day Ann took half of the money plus $1 more. Then Dan took half of the money plus $1 more. Stan then took the remaining $11. How many dollars were originally in the box?

 

Solution
You can avoid some massy algebra by working backwards. Put back the $11 Stan took; then put back the extra $1 that Dan took. There is now $12, which means that, when Dan took his half, he took $12. Put that back. Now there is $24 in the box. Put back the extra $1 that Ann took. The box now has $25, so before Ann took her half, there was $50. The answer is ($50).
17)

Each of the 10 players on the basketball team shot 100 free throws, and the average number of baskets made was 75. When the highest and lowest scores were eliminated the average number of baskets for the remaining 8 players was 79.What is the smallest number of baskets anyone could have made?

Since the average of all 10 players was 75, the total number of baskets made was 10 × 75 = 750. Also, since 8 of the player had an average of 79, they made a total of 8 × 79 = 632 points. The other 2 players, therefore, made 750- 632 = 118 baskets. The most baskets that the player with the highest number could have made was 100, so the player with the lowest number had to have made at least 18.
The answer is 18.
18)

Karen played a game several times. She received $5 every time she won and had to pay $2 every time she lost. If the ratio of the number of times she won to the number of times she lost was 3:2, and if she won a total of $66, how many times did she play the game?

Karen won 3x times and lost 2x times, and thus played a total of 5x games. Since she got $5 every time she won, she received $5(3x) = $15x. Also, since she paid $2 for each loss, she paid out $2(2x) = $4x. Therefore, her net winning were $15x – 4x = $11x, which you are told was $66. Then, 11x = 66 ⇒ x = 6, and so 5x = 30.
The answer is 30
19)

Since 1950, when martin graduated from high school, he has gained 2 pounds every year. In 1980 he was 40% heavier than in 1950. What percent of his 1995 weight was his 1980 weight?

Solution
Let x = Martin’s weight in 1950. By 1980, he had gained60 pounds (2 pounds per
year for 30 years) and was 40% heavier:
60 = 0.40x x = 60 ÷ 0.4 = 150. In 1980, he weighed 210 pounds, 15 years later, in 1995, he weighed 240:
210/240= 7/8= 87.5%. The answer is C.
20)

Henry drove 100 mile to visit a friend. If he had driven 8 mile per hour faster than he did, he would have arrived in of the time he actually toke. How many minute did the trip take?


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