This document contains a review for the mathematics portion of the University of the Philippines-Diliman College Entrance Test. It covers 16 multiple choice questions about integers. The questions test concepts like properties of integers, divisibility rules, consecutive integers, and solving multi-step word problems involving integers and operations like addition, subtraction, multiplication and division. The correct answers to each question are provided at the end.

1. University of the Philippines-
Diliman College Entrance
Test Reviewer
MATHEMATICS
INTEGERS

2. INTEGERS
• Set of numbers containing the whole numbers and their
opposites
• Must be written without a fractional or decimal component
• Usually denoted with the symbol Z

3. QUESTION NO. 1
If x is an integer, which of the following must also be an integer?
I. 8x II.
𝑥
8
III. x-8
a.) I only c.) III only
b.) II only d.) I and III only

4. QUESTION NO. 2
If 𝑥 is an integer, which of the following must also be an
integer?
I. 𝑥 + 16 II. 16𝑥 III.
8
16𝑥
a.) I only c.) III only
b.) II only d.) I and III only

5. QUESTION NO. 3
If x is an integer between 0 and 100, then any of the following
could be 3x + 3, except
a.) 168 c.) 303
b.) 246 d.) 306

6. QUESTION NO. 4
If m is an integer, which of the following must be true
I. 2 𝑚
2 𝑚
= (2 𝑚) 𝑚
II. 𝑚2
𝑚2
= (𝑚2)2
III.2 𝑚
+ 2 𝑚
= 2 𝑚+1
a.) I only c.) III only
b.) II only d.) I and III only

7. QUESTION NO. 5
Which of the following cannot yield an odd integer when divided
by 10?
a. The sum of two odd integers
b. The product of two prime numbers
c. The product of two odd integers
d. The sum of three consecutive integers

8. QUESTION NO. 6
If positive integers m and n are not both even, which of the
following must be odd?
a. 2(m+n) – 5
b. mn
c. m – n
d. m + n – 1

9. QUESTION NO. 7
If a positive integer x is divisible by both 3 and 7, then it is must
also be divisible by what number?
a. 10
b. 21
c. 63
d. 105

10. QUESTION NO. 8
If x, x + 1 and x + 2 represent three consecutive integers that
have the sum of 306, what is x?
a. 100
b. 101
c. 102
d. 103

11. QUESTION NO. 9
The sum of two numbers is 80. What is their greatest product?
a. 400
b. 1600
c. 700
d. 6,400

12. QUESTION NO. 10
The sum of three consecutive even integers is 60. What are these
numbers?
a. 14, 16, 18
b. 16, 18, 20
c. 18, 20, 22
d. 16, 24, 30

13. QUESTION NO. 11
If a and b are different integers, both are divisible by 8, then
which of the following is false?
a. a – b is divisible by 8
b. ab is divisible by 64
c. 𝑎2
+ 𝑏2
is divisible by 8
d. a + b is divisible by 16

14. QUESTION NO. 11
If a and b are different integers, both are divisible by 8, then
which of the following is false?
a. a – b is divisible by 8
b. ab is divisible by 64
c. 𝑎2
+ 𝑏2
is divisible by 8
d. a + b is divisible by 16

15. QUESTION NO. 12
If n is an odd integer, all of the following are odd except?
a. 3n + 4
b. 5𝑛5
+ 𝑛
c. 8𝑛2
+ 𝑛
d. 2𝑛3
+ 3𝑛

16. QUESTION NO. 13
Kung ang
𝑥
𝑦
= 8, alin sa mga sumusunod ang totoo?
a. x ay maaaring maging zero
b. Parehong x at y ay hindi pwedeng maging integers
c. Parehong x at y ay dapat magkapareho ng signs
d. Parehong x at y ay dapat multiples ng 8

17. QUESTION NO. 14
A submarine started out 140 feet below sea level, then after an
hour dives 277 feet before rising 325 feet three hours later. How
many feet is it located in the present?
a. 92 feet below sea level
b. 102 feet below sea level
c. 122 feet below sea level
d. 152 feet below sea level

18. QUESTION NO. 15
The sum of four consecutive even integers is 36, what is the third
largest integer in the set?
a. 6
b. 8
c. 10
d. 12

19. QUESTION NO. 16
If x > 0, which of the following must always be true?
I. 𝑥 < x II. 𝑥2
> 𝑥 III. 𝑥2
> 𝑥
a. I only c. III only
b. II only d. None of the above

20. ANSWERS:
1. D
2. B
3. D
4. D
5. C
6. A
7. B
8. B
9. B
10.C
11.D
12.B
13.C
14.A
15.C
16.D