If $[x]$ denotes the least integer greater than or equal to $x$ and $[x] = 0,$ which of the following statements

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Thu Dec 02, 2021 8:30 am

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If $[x]$ denotes the least integer greater than or equal to $x$ and $[x] = 0,$ which of the following statements must be true?

A. $x = 0$
B. $0 \le x < 1$
C. $0 < x \le 1$
D. $-1 \le x < 0$
E. $-1 < x\le 0$

Answer: E

Source: GMAT Prep

Source: Beat The GMAT — Problem Solving | Thu Dec 02, 2021 8:30 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: If $[x]$ denotes the least integer greater than or equal to $x$ and $[x] = 0,$ which of the following statemen

by Brent@GMATPrepNow » Thu Dec 02, 2021 11:05 am

Vincen wrote: ↑
Thu Dec 02, 2021 8:30 am
If $[x]$ denotes the least integer greater than or equal to $x$ and $[x] = 0,$ which of the following statements must be true?

A. $x = 0$
B. $0 \le x < 1$
C. $0 < x \le 1$
D. $-1 \le x < 0$
E. $-1 < x\le 0$

Answer: E

Source: GMAT Prep

First, let's take a moment to get a good idea of what this strange notation means.
A few examples:
[5.1] = 6 since 6 is the smallest integer that's greater than or equal to 5.1
[3] = 3 since 3 is the smallest integer that's greater than or equal to 3
[8.9] = 9 since 9 is the smallest integer that's greater than or equal to 8.9
[-1.4] = -1 since -1 is the smallest integer that's greater than or equal to -1.4
[-13.6] = -13 since -13 is the smallest integer that's greater than or equal to -13.6

So, if [x] = 0, then -1 < x ≤ 0

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: If $[x]$ denotes the least integer greater than or equal to $x$ and $[x] = 0,$ which of the following statemen

by swerve » Thu Dec 02, 2021 6:17 pm

Vincen wrote: ↑
Thu Dec 02, 2021 8:30 am
If $[x]$ denotes the least integer greater than or equal to $x$ and $[x] = 0,$ which of the following statements must be true?

A. $x = 0$
B. $0 \le x < 1$
C. $0 < x \le 1$
D. $-1 \le x < 0$
E. $-1 < x\le 0$

Answer: E

Source: GMAT Prep

$[x]$ is defined as the least integer greater than or equal to $0$ and $[x]=0$

So, $x$ has to be between $-1$ and $0$

$x$ cannot be equal to $-1$ as $[x] = -1$ in that case and $x$ can be equal to $0$ as in that case also $[x]=0$

So, $-1 < x \leq 0$

So, the correct answer is E

Hope this helps!

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