Numerical Ability Reviewer Part 12 with Answers

Part 12 of our Numerical Ability reviewer has 25 practice questions in the style of the Civil Service Exam. Answer them in order, read the explanation after each one, and check your score against the 80% passing mark at the end. Questions and choices are reshuffled every time you retake the part.

Start Part 12

Sample questions from Part 12

Here are a few questions from this part. Take the full test to answer all 25 and get your score.

Sample question 1

Oil is pumped into a non-empty tank at a changing rate. The volume of oil in the tank doubles every minute and the tank is filled in 10 minutes. How many minutes did it take for the tank to be half full?

Answer: 9

At the 10 minute mark, the tank has twice as much oil in it as it did at the 9 minute
mark. So the tank became half-full at the 9 minute mark.

Sample question 2

Alice and Bill are walking in opposite directions along the same route between A and B. Alice is going from A to B, and Bill from B to A. They start at the same time. They pass each other 3 hours later. Alice arrives at B 2.5 hours before Bill arrives at A. How many hours does it take for
Bill to go from B to A?

Answer: 7.5

Solution: Suppose that it takes Alice x hours to go from A to B. Then, it takes Bill x +2.5 hours to
go from B to A. Assuming that Alice and Bill maintain constant speed, we get that Alice’s speed
is d=x and Bill’s speed is d=(x +2.5), where d is the distance from A to B. Since Alice and Bill
met 3 hours after they started walking,

3 (d / x + d / x + 2.5 ) = d

Dividing by d and solving for x we get x =5, so the answer is 5+2:5=7:5 hours.

Sample question 3

Two armies are advancing towards each other, each one at 1 mph. A messenger leaves the first army when the two armies are 10 miles apart and runs towards the second at 9 mph. Upon reaching the second army, he immediately turns around and runs towards the first army at 9 mph. How many miles apart are the two armies when the messenger gets back to the first army?

Answer: 6.4

The messenger reaches the second army in one hour (the messenger and the second
army advance at each other at a combined speed of 10 mph). At that time, the two armies are 8
miles apart. It takes 0.8 hours for the messenger to get back to the first army. At that time the
armies are 8 - 0:8 -0.8=6.4 miles apart.

Sample question 4

You play on a game show where a prize has been randomly put into one of five boxes, labeled A, B, C, D, and E, with each box equally likely to contain the prize. The boxes are closed when you first see them, and you guess that box A contains the prize. Two of the empty boxes from among the four other boxes are then opened. If these two boxes are C and E, what is the probability that box D contains the prize?

Answer: 2/5

The probability of the prize being in box A is equal to that of it being in any other box;
hence this probability is 1=5. The remaining 4=5 is split between Box D and Box B; hence the
probability that Box D contains the prize is 2=5.

Sample question 5

Six mountain climbers divide themselves into three teams for the final assault on a peak. One team has 3 climbers; the others have 1 and 2 climbers. All manners of different team deployments are considered, which team goes first, second, and third, and two deployments are considered different if the composition of any of the teams is different. (Disregard deployments within each team.) What is the total number of possible team deployments?

Answer: 360

There are six ways to choose which team goes first, which goes second and which 6
goes third. Also, there are = 20 ways to select three climbers out of the six for the three man
team, and 3 ways to pick a climber out of the remaining three for the one man team. So, the
total number of ways is 6 .20 .3 = 360 ways.

Numerical Ability Reviewer - Part 12