For every negative integer y, let [y] be defi… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

For every negative integer y, let [y] be defined as $y^2 - y^3 + y^4$ . Which of the following is equal to $(-3)*[-3]$ ?

Correct answer marked below

(-9) + [81]

[-2]*[-3] - 27

[-1]*[-3]

[-3] + [-2] + 64

[-4] - [-5] + 88

Correct

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Explanation

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Official Explanation

Official

First, calculate [-3] using the definition: [y] =

y^2 - y^3 + y^4

.

For y = -3:

[-3] = (-3)^2 - (-3)^3 + (-3)^4 = 9 - (-27) + 81 = 9 + 27 + 81 = 117

Then compute

(-3)*[-3] = (-3)*117 = -351

Now evaluate each option to see which equals -351.

Option A:

(-9) + [81]

— [81] is not defined since y must be negative. Eliminate.

Calculate other needed values:

[-1] = (-1)^2 - (-1)^3 + (-1)^4 = 1 - (-1) + 1 = 1 + 1 + 1 = 3

[-2] = (-2)^2 - (-2)^3 + (-2)^4 = 4 - (-8) + 16 = 4 + 8 + 16 = 28

…

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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.