If w x^2 ≥ y, which of the following must be true?

Question

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

HKD1710 · Accepted Answer

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

mihir0710 · Answer

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)

ehsan090 · Answer

Bunuel  
Please help when you find time
TIA

HKD1710 · Answer

Hi ehsan090 , would you please post your query? I will certainly try to help you.

niks18 · Answer

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.

chetan2u · Answer

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

ehsan090 · Answer

HKD1710 
Need explanation of option 2 and 3.

shashankism · Answer

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| for 0y 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

saynchalk · Answer

Thanks for taking the approach as per exam scenario!

saynchalk · Answer

Thanks for taking the approach as per exam scenario!

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

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

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