Numerical Ability Reviewer Part 13 with Answers

Part 13 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 13

Sample questions from Part 13

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

Sample question 1

In a class of 100 students, there are 50 who play soccer, 45 who play basketball, and 50 who play volleyball. Only 15 of these students play all three sports. Everyone plays at least one of these sports. How many of the students play exactly two of these sports?

Answer: 15

Let S1 be the number of students who play exactly one of the three sports; S2 – the number of students who play exactly two of the three sports; and let S3 be the number of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100 (the total number of students). Also in the sum 50+45+50 (soccer players + basketball players + volleyball players), each student who plays exactly one sport is counted once,the ones who play exactly two sports are counted twice, and those who play all three sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15.

Sample question 2

Fresh grapes contain 80% water by weight, whereas dried grapes contain15% water by weight. How many pounds of dried grapes can be obtained from 34 pounds of fresh grapes?

Answer: 8

Suppose we call what’s left from a grape after removing all water “waterless content”.
Then 34 pounds of fresh grapes contain 6.8 pounds “waterless content”. Also, x pounds dried
grapes contain x−0.15x = 0.85x pounds “waterless” content”. Solving the equation 0.85x = 6.8
we get x = 8.

Sample question 3

The sum of seven consecutive integers is 980. How many of them are prime?

Answer: 2

The middle number is 140 and the seven numbers are 137, 138, 139, · · · , 143. Now
138, 140, and 142 are even, 141 is divisible by 3, and 143 - by 11. The remaining numbers 137
and 139 are prime (it is easy to check that they are not divisible by 2,3,5,7 and 11).

Sample question 4

It rained on exactly 7 of the days during Jane's summer holiday trip. On each day that it rained, it rained either in the morning or the afternoon but not both. There were exactly 5 afternoons when it did not rain and exactly 6 mornings when it did not rain. How many days did the trip last?

Answer: 9

Let M be the number of days it rained in the morning; A - the number of days it rained
in the afternoon; and let N be the number of days when it did not rain. We have M + A = 7 (days
when it rained); M + N = 5 (afternoons when it did not rain); and A + N = 6 (mornings when it did
not rain). Adding the equations we get 2(M + A + N) = 18, M + A + N = 9.

Sample question 5

Suppose that 25% of all the wise people are nice and half of all the nice people are wise. Suppose further that 25% of all the people are neither wise nor nice. What percent of all the people are both wise and nice?

Answer: 15

Let k be the number of all the people who are both nice and wise. Then, the number of
wise people is 4k and the number of nice people is 2k. The number of people who are either
wise or nice or both is 4k + 2k − k = 5k. If the number of all people is x, then x − 0.25x = 5k, so x
= 20k/3.

Numerical Ability Reviewer - Part 13