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<x> is the largest integer less than or equal to x and [x] is the smal

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6012
GMAT 1: 760 Q51 V42
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<x> is the largest integer less than or equal to x and [x] is the smal  [#permalink]

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17 Jul 2018, 01:12
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Difficulty:

5% (low)

Question Stats:

94% (01:02) correct 6% (01:08) wrong based on 47 sessions

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[GMAT math practice question]

<x> is the largest integer less than or equal to x and [x] is the smallest integer greater than or equal to x. If x is not an integer, which of the following could be the value of [x] - <x>?

A. 1
B. 2
C. 3
D. 4
E. 5

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1201 Location: India GPA: 3.82 <x> is the largest integer less than or equal to x and [x] is the smal [#permalink] Show Tags 17 Jul 2018, 01:18 MathRevolution wrote: [GMAT math practice question] <x> is the largest integer less than or equal to x and [x] is the smallest integer greater than or equal to x. If x is not an integer, which of the following could be the value of [x] - <x>? A. 1 B. 2 C. 3 D. 4 E. 5 Let $$x=I.abc$$, where $$I,a,b,c$$ are some numbers Given $$<x>=I$$ and $$[x]=I+1$$ Therefore $$[x]-<x>=I+1-I=1$$ Option A Manager Joined: 04 Aug 2010 Posts: 234 Schools: Dartmouth College Re: <x> is the largest integer less than or equal to x and [x] is the smal [#permalink] Show Tags 17 Jul 2018, 04:04 MathRevolution wrote: [GMAT math practice question] <x> is the largest integer less than or equal to x and [x] is the smallest integer greater than or equal to x. If x is not an integer, which of the following could be the value of [x] - <x>? A. 1 B. 2 C. 3 D. 4 E. 5 Let x = 0.5. <x> = <0.5> = the largest integer less than 0.5 = 0. [x] = [0.5] = the smallest integer greater than 0.5 = 1. [x] - <x> = 1 - 0 = 1. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Manager Joined: 20 Aug 2015 Posts: 101 Location: India GMAT 1: 710 Q50 V36 GPA: 3 Re: <x> is the largest integer less than or equal to x and [x] is the smal [#permalink] Show Tags 17 Jul 2018, 04:29 <x> is the largest integer less than or equal to x and [x] is the smallest integer greater than or equal to x. If x is not an integer, which of the following could be the value of [x] - <x>? A. 1 B. 2 C. 3 D. 4 E. 5 Pick a number 5.6 [x] - <x> = 6 - 5 = 1 (A) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6012 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: <x> is the largest integer less than or equal to x and [x] is the smal [#permalink] Show Tags 19 Jul 2018, 02:28 => <x> can be defined in the following way: If m ≤ x < m + 1, where m is an integer, then <x> = m. [x] can be defined in the following way: If n – 1 < x ≤ n, where n is an integer, then [x] = n. Since x is not an integer, there is an integer n such that n – 1 < x < n. So, <x> = n -1 and [x] = n. Thus, [x] - <x> = n – ( n – 1 ) = 1. We can also solve this problem by plugging in numbers. If x = 1.1, then [1.1] - <1.1> = 2 – 1 = 1. Therefore, the answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Joined: 04 Jan 2015
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Re: <x> is the largest integer less than or equal to x and [x] is the smal  [#permalink]

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19 Jul 2018, 05:27

Solution

Given:

• <x> is the largest integer less than or equal to x
• [x] is the smallest integer greater than or equal to x

Approach and Working:

Let’s suppose x= n.abc, then:
• <x>= n
• [x]= n+1
o Thus, [x] - <x>= 1

Hence, the correct answer is option A.

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Re: <x> is the largest integer less than or equal to x and [x] is the smal &nbs [#permalink] 19 Jul 2018, 05:27
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