For positive integers x, y, and z, the function x ? y ? z means that zx^y is an integer, but zx^y+1 is not. If x ? 2 ? 144, then which of the following is NOT a possible value of x ?

For positive integers x, y, and z, the functi… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

For positive integers x, y, and z, the function x ? y ? z means that $\frac{z}{x^y}$ is an integer, but $\frac{z}{x^{y+1}}$ is not. If x ? 2 ? 144, then which of the following is NOT a possible value of x ?

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As per the function:

\frac{144}{x^2}

should be an integer and

\frac{144}{x^3}

should NOT be an integer.

Let's test each option:

- x = 2:

x^2 = 4

x^3 = 8

\frac{144}{4} = 36

(integer)

\frac{144}{8} = 18

(integer) → violates condition.

- x = 3:

x^2 = 9

x^3 = 27

\frac{144}{9} = 16

(integer)

\frac{144}{27} = 5.33

(not integer) → satisfies condition.

- x = 4:

x^2 = 16

x^3 = 64

\frac{144}{16} = 9

(integer)…

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.