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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sat Apr 04, 2020 8:35 pm

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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 <= x < 1
C. 0 < x <= 1
D. -1 <= x < 0
E. -1 < x <= 0

OA E

Source: GMAT Prep

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Source: Beat The GMAT — Problem Solving | Sat Apr 04, 2020 8:35 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; 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 statements must be t

by Brent@GMATPrepNow » Sun Apr 05, 2020 5:41 am

BTGmoderatorDC wrote: ↑
Sat Apr 04, 2020 8:35 pm
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 ≤ x < 1
C. 0 < x ≤ 1
D. -1 ≤ x < 0
E. -1 < x ≤ 0

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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8177; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If [x] denotes the least integer greater than or equal to x and [x] = 0, which of the following statements must be t

by Scott@TargetTestPrep » Thu Apr 09, 2020 4:04 am

BTGmoderatorDC wrote: ↑
Sat Apr 04, 2020 8:35 pm
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 <= x < 1
C. 0 < x <= 1
D. -1 <= x < 0
E. -1 < x <= 0

OA E

Source: GMAT Prep

We are given that [x] denotes the least integer greater than or equal to x and that [x] = 0.

So some numbers x can be include: 0, -0.1, -0.5, -0.9 and -0.999.

Thus, we see that x must be strictly greater than -1 but less than or equal to 0.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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