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If w > x^2 ≥ y, which of the following must be true?
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21 Mar 2017, 05:42
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48% (01:39) correct 52% (01:44) wrong based on 222 sessions
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If w > x^2 ≥ y, which of the following must be true? I. x ≥ 0 II. w > x III. w > y ≥ x A. None B. II only C. I and II only D. I and III only E. I, II and III
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Re: If w > x^2 ≥ y, which of the following must be true?
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21 Mar 2017, 06:09
Bunuel wrote: If w > x^2 ≥ y, which of the following must be true?
I. x ≥ 0 II. w > x III. w > y ≥ x
A. None B. II only C. I and II only D. I and III only E. I, II and III w>x^2 => w > x …..so II is correct x can be greater than zero or can be –ve ….so I may or may not be true in all cases Since x and y are NOT necessarily integers, y>=x may NOT be true in some cases …so III may or may not be true…. Hence Option B (II only)
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If w > x^2 ≥ y, which of the following must be true?
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21 Mar 2017, 11:27
mihir0710 wrote: Bunuel wrote: If w > x^2 ≥ y, which of the following must be true?
I. x ≥ 0 II. w > x III. w > y ≥ x
A. None B. II only C. I and II only D. I and III only E. I, II and III w>x^2 => w > x …..so II is correct x can be greater than zero or can be –ve ….so I may or may not be true in all cases Since x and y are NOT necessarily integers, y>=x may NOT be true in some cases …so III may or may not be true…. Hence Option B (II only) w > x^2 what if w=1/3 and x=1/2 or 1/2 x > w > x^2 1/2 > 1/3 > 1/4 Hence II. w > x is not MUST BE TRUE. Pattern: whenever a variable is compared with other variable having exponent then: 1. check whether variable with exponents can be a fraction 2. check the whether the exponent is even or odd to decide the sign 3. What about the mod of the variable with even exponent
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Re: If w > x^2 ≥ y, which of the following must be true?
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15 Apr 2017, 23:12
Bunuel Please help when you find time TIA
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Re: If w > x^2 ≥ y, which of the following must be true?
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15 Apr 2017, 23:59
ehsan090 wrote: Bunuel Please help when you find time TIA Hi ehsan090, would you please post your query? I will certainly try to help you.
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If w > x^2 ≥ y, which of the following must be true?
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Updated on: 18 Apr 2017, 11:15
Correct me if I am wrong here As per question  w>x^2>=y since x^2 cannot be negative but x can be negative for e.g x=2. Question stem does not reveal any information regarding "y". Hence Statement I might or might not be true Statement II does not work for fractions. If w=1/3 and x=1/2 then w>x^2 but w<x Statement III does not work for irrational nos. for example if y=2 and x = \sqrt{5}. In this case x^2>=y is satisfied but statement III is not satisfied.
Originally posted by niks18 on 16 Apr 2017, 03:42.
Last edited by niks18 on 18 Apr 2017, 11:15, edited 1 time in total.



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Re: If w > x^2 ≥ y, which of the following must be true?
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16 Apr 2017, 03:59
Bunuel wrote: If w > x^2 ≥ y, which of the following must be true?
I. x ≥ 0 II. w > x III. w > y ≥ x
A. None B. II only C. I and II only D. I and III only E. I, II and III Hi, If it were a part of exam and time is important\(w>x^2\geq{y}\) x ≥ 0 should immediately tell us that x^2 should be POSITIVE but there is no reason why x ≥ 0. Thus I is surely not MUST be true. If I is taken out, all choices except A and B can be eliminated. We have to just check for II now. w>x Since x can be a fraction between 0and 1.... Here we need not be greater than x example  x is 1/2 and y is 1/3.... y>x^2 but y<x... If x is ive or greater than 1.. y will be greater than x if y>x^2.. Hence II need not be true always.. ONLY option left is A.. A
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Re: If w > x^2 ≥ y, which of the following must be true?
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16 Apr 2017, 05:57
HKD1710 wrote: ehsan090 wrote: Bunuel Please help when you find time TIA Hi ehsan090, would you please post your query? I will certainly try to help you. HKD1710Need explanation of option 2 and 3.
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Re: If w > x^2 ≥ y, which of the following must be true?
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02 Aug 2017, 02:43
Bunuel wrote: If w > x^2 ≥ y, which of the following must be true?
I. x ≥ 0 II. w > x III. w > y ≥ x
A. None B. II only C. I and II only D. I and III only E. I, II and III w > x^2 ≥ y So, w must be +ve I. x can be ve or +ve , we can't say anything about x II. w > x^2 So for 1<x<infinity , w >x for 0<x<1, w may or may not be greater than x. III. w>y this may or may be possible Similarly y>/x this may or may not be possible. So None of the I, II,III are correct. Answer A
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29 Sep 2018, 12:42
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Re: If w > x^2 ≥ y, which of the following must be true?
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