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If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]
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29 Aug 2014, 06:09
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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
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Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]
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29 Aug 2014, 06:18
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[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 <= 0 So, Answer will be E Hope it helps! goodyear2013 wrote: 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
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If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]
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29 Aug 2014, 06:22
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Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]
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29 Aug 2014, 06:24



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Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]
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01 Oct 2014, 21:00
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goodyear2013 wrote: 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 The answer for this is 0 < = x < = 1However it is not available in the options. The match to the above is 1 < x <= 0Answer = E
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Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]
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30 Mar 2015, 09:13
Bunuel wrote: goodyear2013 wrote: 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 Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [1.5]=1, ... Hence, since [x] = 0, then it must be true that \(1x\leq{0}\): any number from this range when rounded up gives 0. Answer: E. Hi Bunuel So just to clarify, if x = 1, then [x] = 1 But since its given that [x] = 0, hence x can be at the least 0.99 and max 0I think the trap here is greater than or equal to x Thats why "D" is wrong Is this understanding correct? Thanks



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Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]
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31 Mar 2015, 03:04
goodyear2013 wrote: 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 Least integer GREATER THAN or EQUAL to x means [x] when rounded off to the nearest integer is GREATER THAN or EQUAL to [x]. Given that [x] = 0 So, [x] can take any value from 1 to 0 (excluding 1 and including 0), it will always be equal to 0. Hence option (E).  Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimusprep.com/gmatondemandcourse



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Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]
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31 Mar 2015, 03:47
buddyisraelgmat wrote: Bunuel wrote: goodyear2013 wrote: 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 Some function [] rounds UP a number to the nearest integer. For example [1.5]=2, [2]=2, [1.5]=1, ... Hence, since [x] = 0, then it must be true that \(1x\leq{0}\): any number from this range when rounded up gives 0. Answer: E. Hi Bunuel So just to clarify, if x = 1, then [x] = 1 But since its given that [x] = 0, hence x can be at the least 0.99 and max 0I think the trap here is greater than or equal to x Thats why "D" is wrong Is this understanding correct? Thanks [x] = 0, means that \(1<x\leq{0}\): any number from this range when rounded up gives 0. D is wrong because x can be 0, while D excludes this possibility.
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Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]
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29 May 2015, 18:20
E totally makes sense and I went for that option as well but can someone explain why A is wrong?



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Re: If [x] denotes the least integer greater than or equal to x and [x] = [#permalink]
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29 May 2015, 20:14
Hi healthjunkie, When a question asks "which of the following statements MUST be true?", you can interpret this to mean "which of the following statements is ALWAYS TRUE no matter how many different examples we can come up with?" In this question, we're told that [X] is the least integer GREATER THAN OR EQUAL to X. We're also told that [X] = 0. So, while X = 0 is a potential value for X (since 0 is the least integer that is greater than or equal to 0), it is NOT the only potential value. As an example, X COULD be 1/2 The least integer that is greater than or equal to 1/2 IS 0. Thus, Answer A is NOT always true. With these types of questions, you have to make sure that you're doing enough work to prove when something is ALWAYS true vs. when something is SOMETIMES true. GMAT assassins aren't born, they're made, Rich
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