MATH PROF

If 6 < a < 10 and 8 < b < 16, what are the possible values of a + 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.

c) a + b must be between 5 and 26.

The absolute value of the difference of the cubes of any two consecutive positive integers is always a) an even integer b) the cube of an integer c) an odd integer d) a multiple of 3

c) an odd integer

If a, b, c, d and e are divisible by 8, then their average must be a) divisible by 8 b) divisible by 4 c) divisible by 2 d) none of these

c) divisible by 2

If n = -1 000 000, which of the following is a positive number? a) 𝑛/4 = 𝑛/8 b) 𝑛/2 = 𝑛/4 c) 𝑛/8 = 𝑛/4 d) - n(n - 100)

d) - n(n - 100)

Find the ratio x : y if x : y : 4/5 = 3/5 : 1/10 : 7/15 a) 3 : 1 b) 1 : 3 c) 6 : 1 d) 1 : 6

d) 1 : 6

If z = 3/8 - 9/24 + 15/40 , then (z - 1)^3 = ? a) - 5/8 b) 5/8 c) - 125/512 d) 125/512

BONUS

What is the units digit of the product of the first 1 000 smallest prime numbers? a) 0 b) 1 c) 2 d) 5

a) 0

If 7 and 11 divide M without a remainder, which of the following must M divide without a remainder? a) 1 b) 77 c) 7 d) can't be determined form the given information

a) 1

Given that a : b = 3 : 1 and b : c = 2 : 3, find the ratio of a : c. a) 1 : 1 b) 2 : 1 c) 1 : 2 d) 3 : 2

a) 1 : 1

If x is an integer such that 3 < x < 23, - 6 < x < 16, 14 < x < 27, and 0 < x + 20 < 38 then x is a) 10 b) 15 c) 18 d) 22

a) 10

Density is mass per unit volume. Find the mass of a solid copper bar that occupies a volume of 1200 cm3 , given that the density of copper is 8.93 gram per cubic centimeter. a) 10 716 g b) 10 716 cm^3 c) 134.8 g d) 134.38 cm^3

a) 10 716 g

If 988 × 1012 > 106 - x, 'x could be a) 144 but not 100 b) 100 but not 144 c) 150 but not 144 d) 88 but not 12

a) 144 but not 100

√ (𝑥^2)/25 + (𝑥^2)/144 = ? a) 17/60 | x | b) 13/60 | x | c) 17/60 x d) 13/60 x

a) 17/60 | x |

What is the greatest possible value of 𝑥+𝑦 𝑥𝑦 if 8 ≤ x ≤ y ≤ 16? a) 17/72 b) 31/240 c) 6/16 d) 17/36

a) 17/72

If x is an odd integer, which of the following expressions is even? a) 2x 3 - x b) 8x 2 + x c) 5x - 8 d) 5x 9 + x

a) 2x 3 - x

If 4x + y = 18, and x and y are positive integers, each of the following could be the value of x + y, except a) 3 b) 9 c) 12 d) 15

a) 3

How many positive integers less than 100 are equal to the product of a positive multiple of 5 and an even number? a) 4 b) 5 c) 9 d) 10

a) 4

At what time after 4:00 will the minute hand and the hour hand of a clock first be in the same position? a) 4 : 20 : 09 b) 4 : 22 : 49 c) 4 : 21 : 49 d) 12 : 00 : 00

a) 4 : 20 : 09

If n is a natural number, which of the following could be an odd integer? a) 4n - 2 b) n^2 + n c) 9n + 3 d) n^8 + n

a) 4n - 2

Let N = √( 1/3 + 1/9 + 1/27 + 1/81) + ( 1/9 + 5/27) . N is also equal to a) 8/9 b) 7/9 c) 5/9 d) 1/27

a) 8/9

Which combination of the following statements can be used to demonstrate that a is positive? I. a > b II. 0 < b < 1 a) I alone but not II. b) Both I alone and II alone. c) Neither I nor II nor both. d) I and II taken together but neither taken alone.

a) I alone but not II.

If x is an odd number, then which of the following best describes the number represented by x 2 + 2x + 2? a) It must be odd. b) It must be even. c) It must be divisible by 3. d) It can be odd or even.

a) It must be odd.

The quotient of ( 9.6 × 108 ÷ 1.92 × 108 ) is a) greater than 2 × 108 b) an even number c) less than 2 d) a prime number

a) greater than 2 × 108

The unit price of an article rises 20% from p to P84. The profit for selling these articles is (80 - p)pesos per piece. Find the gross profit for 100 units sold? a) P 10 b) P 100 c) P 1 000 d) P 70

c) P 1 000

Water freezes at 0°Celsius and at 32°Fahrenheit. Water boils at 100°C and 212°F. What Celsius temperature corresponds to - 40°F? a) 172°C b) - 40°C c) 252°C d) - 252°C

b) - 40°C

What is the second smallest two-digit number that has an odd number of factors? a) 10 b) 16 c) 25 d) 99

b) 16

How many digits are there in the product 2^(2001) × 5^(2002)? a) 2000 b) 2001 c) 2002 d) 4003

b) 2001

If x < 0 and (8x - 8)2 = 144, what is the value of x 2 ? a) - 5/4 b) 25/4 c) 5/2 d) - 5/2

b) 25/4

What is one-ninth of 3^(81)? a) 379 b) 39 c) 327 d) 927

b) 39

. If x ≠ 0, then which of the following must be true? a) x^3 > x b) 3x > x c) x + 2 > x d) - x < x

b) 3x > x

The reciprocal of 5 plus the reciprocal of 8 is the reciprocal of what number? a) 13/40 b) 40/13 c) 3/40 d) 2/13

b) 40/13

Evaluate the expression a^b - b^c + (abc)^a if a = 8, b = 2 and c = 0 a) 15 b) 63 c) 64 d) 88

b) 63

If the average (arithmetic mean) of eight different integers is 8, which of the following can be true? I. 8 is one of the integers. II. 0 is not one of the integers. III. At least one of the integers is negative. a) I only b) II only c) III only d) I, II & III

b) II only

Which of the following inequalities is true for every real number? a) x^2 + 16 > 16x b) x^2 - 16 < 16x c) x^2 + 16 ≥ 0 d) x^2 + 16 < 0

b) x^2 - 16 < 16x

If Rochelle were 52 years older, she would be five times as old as she is now. How old is Rochelle now? a) 8 b) 13 c) 15 d) 18

bonus

If a, b, and c are non-zero numbers such that a < b < 1 and ab = c, which of the following is always false? a) c < b c) a = c

bonus

Of the fractions 3/8 , 5/51 , 10/18 and 4/29 , which one is the greatest? a) 3/8 b) 5/51 c) 10/18 d) 4/29

c) 10/18

Twenty pints of 15% alcohol solution is mixed with 10 pints of 20% alcohol solution. What is the concentration of the resulting solution? a) 15% b) 16.67% c) 17.5% d) 18%

c) 17.5%

. Find the sum of the angle measures at the tips of the star shown in the figure. A a) 90° c) 180° b) 72° d) 360°

c) 180°

(1010) 2 in standard form has 20 zeros. How many zeros written in standard form does (10^10 - 1)^2 have? a) 0 b) 1 c) 19 d) 20

c) 19

If 2 ≤ a ≤ 6 and 6 ≤ b ≤ 8, then the greatest possible average (arithmetic mean) of 1 𝑎 and 1 𝑏 is a) 7/24 b) 7/48 c) 2/3 d) 1/12

c) 2/3

Find the largest prime divisor of ( 2^(16) - 1 ). a) 13 b) 17 c) 257 d) 65 535

c) 257

Which of the following numbers is prime? a) 189 b) 209 c) 311 d) 411

c) 311

One of the printing machine of Gerpress Printing, the official printing press of MSA Academic Advancement Institute, can print an order of 5 000 test booklet in 3 hrs. Another machine can print the same number of booklets in 6 hrs. How long will it take to print 5 000 booklets if both machines are used? a) 2 hrs. b) 3 hrs. c) 4.5 hrs. d) 9 hrs

c) 4.5 hrs.

If the following numbers are arranged from least to greatest, what will be their correct order? I. 7 12 II. 12 7 III. 88% IV. 1 0.12 a) I, III, IV, II b) I, II, IV, III c) I, III, II, IV d) IV, II, III, I

c) I, III, II, IV

One number exceeds another by 8, and the sum of the smaller and twice the larger is 40. Find the product of the two numbers. a) 8 b) 16 c) 32 d) 128

d) 128

If a + b = 11, b + c = 15 and a + c = 10, what is the value of a + b + c? a) 18 b) 20 c) 24 d) 36

d) 36

How many ordered pairs of integers (x, y) satisfy x^2 + y^2 < 16? a) 9 b) 16 c) 25 d) 49

d) 49

The weight of a plastic pail is 20% of the weight when it is filled with water. After a certain amount of water has been poured out, the weight of the pail and the remaining water is 60% of the original total weight. What percent of the water remained in the pail? a) 20% c) 40% b) 25% d) 50%

d) 50%

If 2/(𝑥+ 7) = 6 6/11 , then 2/(𝑥+8) = ? a) 1 25/47 b) 7 6/11 c) 47/36 d) 6 6/12

d) 6 6/12

What is the smallest number greater than 1 that leaves a remainder of 1 when divided by any of the integers 5, 6, and 12? a) 13 b) 31 c) 43 d) 61

d) 61

If 3√3 ^3 + 3 ^3 + 3 3 + ⋯ + 3^ 3 3= 3^3 , how many times must 3^3 appear in the radicand? a) 9 b) 27 c) 81 d) 729

d) 729

f M and N are different integers, both divisible by 7, then which of the following is not necessary true? a) MN is divisible by 49 b) M - N is divisible by 7 c) M2 + N2- is divisible by 7 d) M + N is divisible by 14

d) M + N is divisible by 14

If x is an even integer and if y is an odd integer, then x 2 + y 2 is always a) an even integer b) a square of an integer c) an odd number d) a prime number

d) a prime number

What is the greatest common factor of the products ab, ac, and bc, if b is a factor of c? a) a b) b c) c d) can't be determined

d) can't be determined

If n is an integer, which of the following cannot be an integer? a) 𝑛/7 b) √𝑛/7 c) 7n^2 d) n√7

d) n√7

If (x^3 + 3x^2 )^4 = y and x(x + 3) ≠ 0, then 𝑦/(𝑥+3)^4 = ? a) x b) x^2 c) x^4 d) x^8

d) x^8

Find the sum of 800√8 8 − 799√8 8 + 798√8 8 − 797√8 8 + ⋯ − √8 8 . a) 400√8 b) 200√8 c) 100√8 d) √8

d) √8