MATHEMATICS 11.

Find the sum of:

800 8√ 8 – 799 8√ 8 + 798 8√ 8 – 797 8√ 8 + … - 8√ 8
This is a test of your ability to think out solutions to
quantitative problems in Mathematics. Analyze and a. 400 8√ 8 b. 200 8√ 8 c. 100 8√ 8 d. 8√ 8
solve each problem carefully. Determine the best
answer from the four choices a, b, c, d. 12. Evaluate the expression ab – bc + (abc)a if a = 8,
b = 2 and c = 0.
1. What is the units digit of the product of the first
1000 smallest prime numbers? a. 15 b. 63 c. 64 d. 88

a. 0 b. 1 c. 2 d. 5 13. Given that a : b = 3 : 1 and b : c = 2 : 3, find the

ratio of a : c
2. What is the second smallest two-digit number
that has an odd number of factors? a. 1 : 1 b. 2 : 1 c. 1 : 2 d. 3 : 2

a. 10 b. 16 c. 25 d. 99 14. If 7 and 11 divide M without a remainder, which

of the following can M divide without a remainder?
3. The quotient of (9.6 x 108 – 1.92 x 108) is ______
a. 1 b. 6 c. 77 d. It cannot be determined
a. greater than 2 x 108 c. less than 2
b. an even number d. a prime number 4 3 1 7
15. Find the ratio x : y if x : y : = : : .
5 5 10 15
4. Of the fractions 3 , 5 , 10 , and 4 , which one is
the greatest 8 51 18 29 a. 3 : 1 b. 1 : 3 c. 6 : 1 d. 1 : 6
a. 3/8 b. 5/51 c.10/18 d. 4/29 16. If x is an odd integer, which of the following
expression is even?
5. Find the largest prime divisor of (216-1).
a.2x3-x b.8x2+x c.5x-8 d. 5x9+x
a. 13 b. 17 c. 257 d. (215-1)
3 9 15
6. What is one-ninth of 381? 17. If z = − + ; then (z-1)3 ______.
8 24 40
a. 379 b. 39 c. 327 d. 927
−5 −125
a. b. 5/8 c. d. 125/512
7. What is the greatest common factor of the 8 512
products ab, ac, and bc, if b is a factor of c?
18. The unit price of an article rises 20% from p to
a. a b. b c. c d. It cannot be determined P 84. The profit for selling these article is (80-p)
pesos per piece. Find the gross profit for 100 units
8. How many digits are there in the product 22001 x sold.
52002?
a. P 10 b. P 12 c. P 1000 d. P 7200
a. 2000 b. 2001 c. 2002 d.4003
2 6 2
19. If =6 , then = _____
9. If √ 3 +3 +3 ..+3 = 3 , how many times must 3
3 3 3 3 3 3 3 x+ y 11 x+ 8
appear in the radicand? 25 6 47 6
a. 1 b. 7 c. d. 6
47 11 36 12
a. 3 b. 9 c. 27 d. 729
20. If n is an odd number, which of the following
10. Which of the following numbers is prime? could be an odd integer?

a. 189 b. 209 c. 311 d. 411 a. 4n-2 b. n5+n c. 9n+3 d. n8+n

21. The absolute value of the difference of the a. 3 b. 9 c. 12 d. 15
cubes of any two consecutive positive integers is
always _____. 31. If x¿0 and (8x-8)2 = 144, what is the value of x2?
a. an even integer c. an odd integer
b. the cube of an integer d. a multiple of 3 −5
a. b. 25/4 c. 5/2 d. ¼
4
22. Which combination of the following statements
can be used to demonstrate that a is positive? 32. If 2 ≤ a ≤ 6 and 6 ≤ b ≤ 8, then the greatest
possible average (arithmetic mean) of 1/a and 1/b
I. a ¿ b II. 0 ¿ b ¿ 1 is ______.
a. I alone but not II.
b. Both I alone and II alone a. 1/3 b. 7/48 c. 2/3 d. 1/12
c. Neither I nor II nor both
d. I and II taken together but neither taken 33. One number exceeds another by 8, and the
alone. sum of the smaller and twice the larger is 40. Find
the product of the two numbers.
y
23. If (x3+3x2)4 = y and x (x+3) ≠ 0, then =
( x+3 )4 a. 8 b. 16 c. 32 d. 128
a. x b. x2 c. x4 d. x8
34. If n = - 1000000, which of the following is a
x+ y positive number?
24. The greatest possible value if 8 ≤ x ≤ y ≤
xy
16 is ______. n n n n
a. ∎ c. ∎
1 31 6 17 4 8 8 4
a. b. c. d.
4 240 16 36
n n
b. − d. – n (n-100)
25. If 988 x 1012 ¿ 10 – x, could be ______
6 2 4
a. 144 but not 100 c. 150 but not 144
b. 100 but not 144 d. 88 but not 12 35. If x is an even integer and if y is an odd integer,
26. If a, b, c, d, and e are each divisible by 8 then then x2+y2 is always ______.
their average will not be _______.
a. divisible by 8 c. divisible by 2 a. an even integer c. an odd integer
b. divisible by 4 d. None of these b. a square of an integer d. a prime number

27. If x is an odd number, then which of the 36. Mark and Kriselle are 23 and 20 years old
following best describes the number represented by respectively. How many years ago when twice the
x2+2x+2? age of Mark was 10 less than thrice the age of
a. It must be odd c. It must be divisible by 3 Kriselle?
b. It must be even d. It can be odd or even
a. 4 b. 6 c. 8 d. 10
28. If a + b = 11, b + c = 15 and a + c = 10, what is
the value of a + b + c? 37. If x ≠ 0, then which of the following must be
true?
a. 18 b. 20 c. 24 d. 36
a. x3¿x b. 3x¿x c. x+2¿x d. -x¿x
29. If n is an integer, which of the following cannot
be an integer? 38. How many ordered pairs of integers (x,y) satisfy
x2+y2¿16?

a.
n
b.
√n c. 7n2 d. n√ 7
7 a. 9 b. 16 c. 25 d. 45
7

30. If 4x+y = 18, and x and y are positive integers,

each of the following could be the value of x + y
39. Let N =
(√ 13 + 19 + 271 + 811 )+( 19 + 275 )
except _______. N is also equal to _______.
a. 8/9 b. 7/9 c. 5/9 d. 1/27

40. If 6 ¿ a ¿ 10 and 8 ¿ b ¿ 16, what are the

possible values + b?

a. a + b must be equal to 22
b. a + b must be between 6 and 16
c. a + b must be between 5 and 26
d. a + b must be between 14 and 26