If [z] denotes the least integer greater than… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Functions

If [z] denotes the least integer greater than or equal to z and $[z^2]$ = 2, which of the following could be the value of [z]?
I. 2
II. 1
III. -2

Answer Choices

Correct answer marked below

I only

Correct

II only

III only

I and II only

II and III only

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Explanation

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Official Explanation

Official

Official Solution Given:

• The function [z]

•

[z^2] = 2

To find: Can [z] be {2, 1, -2}?

Approach:

• To find which values of [z] are possible and which are not, we need to first know the range of possible values of z. Once we know what z can be, we’ll be able to find what [z] can be.

• We’ll get an idea of the possible values of z from the fact that

[z^2] = 2

Working Out:

•

[z^2] = 2

• This means the least integer that is greater than or equal to

z^2

is 2.

• We can write:

1 < z^2 ≤ 2

• The above inequality contains 2 inequalities:

z^2 > 1

AND

z^2 ≤ 2

So now, we’ll solve these inequalities one by one, and then find the values of z that satisfy both these inequalities.

• Solving

z^2 > 1

:…

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What this question tests

What it tests

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

Common trap

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

If [z] denotes the least integer greater than or equal to z and [z2][z^2][z2] = 2, which of the following could be the value of [z]?I. 2II. 1III. -2