For all values, [x] denotes the least integer… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

For all values, $[x]$ denotes the least integer greater than or equal to x. If $-2.5 < x < 1.5$ , what is the least possible value of $[2x] + [x^2]$ ?

Correct answer marked below

-2

-1

Correct

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Official Explanation

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-2.5 < x < 1.5

, what is the least possible value of

[2x] + [x^2]

?

Let

[x] = -3, -2, -1, 0, 1

(possible integer values for the ceiling function within the range).

Case 1:

[x] = -3

[2x] + [x^2]

[-6] + [9]

-6 + 9 = 3

(not the least value).

Case 2:

[x] = -2

[2x] + [x^2]

[-4] + [4]

-4 + 4 = 0

(not the least value).…

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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.