Mathematics CET practice exam

If n is an odd integer, which one of the following is an even integer

• 2n + 3

• 2n (n + 3)

Answer explanation

We are told that n is an odd integer. So choose an odd integer for n, say, 1 and substitute it into each answer-choice. Now, n ^ 3 becomes 1 ^ 3 = 1 which is not an even Integer. So eliminate (A). Next, n / 4 -> 1/4 Is not an even integer-eliminate (B). Next, 2n + 3 = 2 1 + 3 = 5 is not an even integer-eliminate (C). Next, 2n(n+3)=2^ 1(1 + 3) = 4 is even and hence the answer is possibly (D).

What should be multiplied to the binomial x - y so that the product is a trinomial?

• 10y

• 3x - 5y

• x + y

If p and q are positive integers, how many integers are larger than pq and smaller than p (q + 2)?

• 3

• p + 2

• p - 2

• 2p - 1

Answer explanation

Let p = 1 and q = 2 Then pq = 2 and p(q + 2) = 4 This scenario has one integer, 3, greater than pq and less than p(q + 2) Now, we plug p = 1 and q = 2 into the answer-choices we find one that has the value 1. Look at choice (D): 2p - 1 = (2)(1) - 1 = 1 Thus, the answer is (D).

What is the value of x?

• 30

• 39

• 45

• 60

Answer explanation

Since 2x + 60 is an exterior angle, it is equal to the sum of the remote interior angles. That is, 2x + 60 = x + 90 Solving for x gives x = 30 The answer is (A).

Speed bumps are being placed at 25 foot intervals along a road 1015 feet long. If the first speed bump is placed at one end of the road, how many speed bumps are needed?

• 39

• 40

• 41

• 52

Answer explanation

Since the road is 1015 feet long and the speed bumps are 25 feet apart, there are 1015/25 = 40.6 or 40 full sections in the road. If we ignore the first speed bump and associate the speed bump at the end of each section with that section, then there are 40 speed bumps (one for each of the fifty full sections). Counting the first speed bump gives a total of 41 speed bumps. The answer is (C).

A particular carmaker sells four models of cars, and each model comes with 5 options. How many different types of cars does this carmaker sell?

• 10

• 15

• 20

• 35

Answer explanation

For the first model, there are 5 options. So there are 5 different types of cars in this model. For the second model, there are the same number of different types of cars. Likewise, for the other two types of models. Hence, there are 5 + 5 + 5 + 5 = 20 different types of cars. The answer is (C).

Bowl Z contains only marbles. If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity. If 100 marbles were added, the bowl would be full. How many marbles are in bowl Z?

• 120

• 200

• 250

• 300

Answer explanation

Let x be the number of marbles in bowl Z. We know that 1/2 (x) + 100 = x from the two statements provided. Solving for x, we have x = 200

The buyer of a particular car must choose 2 of 3 optional colors and 3 of 4 optional luxury features. In how many different ways can the buyer select the colors and luxury features?

• 9

• 12

• 15

• 24

Answer explanation

Let A, B, C stand for the three colors, and let W, X, Y, Z stand for the four luxury features. There are three ways of selecting two colors: A-B, B-C, A-C. There are four ways of selecting three luxury features: W-X-Y, W-Y-Z, W - X - Z X-Y-Z. Hence, there are 3 * 4 = 12 ways of selecting all the features. The answer is (B).

Oble runs at least 10km everyday on a circular track. If the track has a diameter of 1km, approximately how many rounds does Oble jogs everyday?

• 2

• 3

• 5

• 7

Answer explanation

Circumference = 2*pi*radius = pi*diameter

C = 3.14 * 1km

C ~3.14km; No. of rounds = distance/circumference

This means 10km/3.14km ~ 3 rounds. The answer is (A)