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Re: If w > x^2 ≥ y, which of the following must be true? [#permalink]

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21 Mar 2017, 05:09

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….

If w > x^2 ≥ y, which of the following must be true? [#permalink]

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21 Mar 2017, 10:27

1

This post was BOOKMARKED

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
_________________

If w > x^2 ≥ y, which of the following must be true? [#permalink]

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16 Apr 2017, 02:42

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This post was BOOKMARKED

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.

Last edited by niks18 on 18 Apr 2017, 10:15, edited 1 time in total.

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..

Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

Re: If w > x^2 ≥ y, which of the following must be true? [#permalink]

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02 Aug 2017, 01:43

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.