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QUESTION: 1

What is the cube root of *w*?

1) The 5^{th} root of *w* is 64

2) The 15^{th} root of *w* is 4

Solution:

QUESTION: 2

Which of the following is equal to (2^{12} – 2^{6})/(2^{6} – 2^{3})?

Solution:

QUESTION: 3

If s^{4}v^{3}x^{7} < 0, is svx < 0?

1) v < 0

2) x > 0

Solution:

QUESTION: 4

What is the value of 2 + 2 + 2^{2} + 2^{3} + 2^{4} + 2^{5} + 2^{6} + 2^{7} + 2^{8}?

Solution:

QUESTION: 5

What is the units digit of 1 + 2^{2} + 3^{3} + 4^{4} + 5^{5}?

Solution:

QUESTION: 6

What is the units digit of 1! + 2! + 3! + 4!?

Solution:

QUESTION: 7

What is the units digit of 1! + 2! + 3! + 4! + 5! + 6! + 7! + 8! + 9! + 10!?

Solution:

QUESTION: 8

What is the units digit of (5!)^{5!}?

Solution:

QUESTION: 9

What is the units digit for (173)^{4} – 1973^{3^2}, where 3^2 means 3 to the power of 2?

Solution:

QUESTION: 10

What is the value of 5 + 4*5 + 4*5^{2} + 4*5^{3} + 4*5^{4} + 4*5^{5}?

Solution:

QUESTION: 11

If x is a positive integer, then the value of (22^{22x} – 22^{2x})/(11^{11x} – 11^{x}) is closest to which of the following:

Solution:

QUESTION: 12

If 4^{-x} + 4^{-x }+ 4^{-x} + 4^{-x} = 1, what is the value of x?

Solution:

QUESTION: 13

Positive integers x, y, and z satisfy the equations x^{-1/2} = 1/3 and y^{z} = 16. If z > y, what is the value of x + z?

Solution:

QUESTION: 14

3x^{2} < (3x)^{2}

For what value of x is the statement above false?

Solution:

QUESTION: 15

If 18√18 = r√t, where r and t are positive integers and r > t, which of the following could be the value of rt?

Solution:

QUESTION: 16

If a, b, and c are positive integers such that 2^{a}*2^{b}*2^{c} = 64, then 2^{a} + 2^{b} + 2^{c} =

Solution:

QUESTION: 17

If a, b, and c are positive integers such that 2^{a} + 2^{b} + 2^{c} = 64, which of the following is a possible value for 2^{a}*2^{b}*2^{c} =

Solution:

QUESTION: 18

If k, n , x, and y are positive integers satisfying x^{-4/3} = k^{-2} and y^{4/3} = n^{2}, what is the value of (xy)^{-2/3} in terms of n and k?

Solution:

QUESTION: 19

If x and y are integers such that x^{2} = 64 and y^{3} = 64, which of the following could be true?

I. x = 8 II. y = -4 III. x + y = -4

Solution:

QUESTION: 20

If (x – 2)^{2} = 49, which of the following could be the value of x?

Solution:

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