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# [a] denotes the greatest integer less than or equal to 'a', for any

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1428
Location: India
[a] denotes the greatest integer less than or equal to 'a', for any  [#permalink]

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26 Jul 2018, 10:41
00:00

Difficulty:

95% (hard)

Question Stats:

28% (03:34) correct 72% (02:11) wrong based on 18 sessions

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[a] denotes the greatest integer less than or equal to 'a', for any real number 'a'. If x is a real number, what is [2x] - [x/2] ?

(1) 1.5 < x < 2.5

(2) x > 2
Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: [a] denotes the greatest integer less than or equal to 'a', for any  [#permalink]

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26 Jul 2018, 17:15
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[a] denotes the greatest integer less than or equal to 'a', for any real number 'a'. If x is a real number, what is [2x] - [x/2] ?

(1) 1.5 < x < 2.5
a) 1.5 <x< 2....
2x will be >3 and <4, so [2x]=3 AND x/2 will be between 0.75 and 1 so [x/2]=0... Ans 3-0=3
b) at 2..
[2x]=4 and [x/2]=1.... Again 4-1=3
c) 2<x<2.5....
[2x]=4 and [x/2]=1.....again 4-1=3

Irrespective of value of X, Ans is 3
Sufficient

(2) x > 2
Insufficient clearly

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: [a] denotes the greatest integer less than or equal to 'a', for any &nbs [#permalink] 26 Jul 2018, 17:15
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