Is x y ? (1) x = 4y^2 (2) x 1

Question

Is x > y ?

(1) x = 4y^2
(2) x > 1

Bunuel · Answer

Is x > y ?

(1) x = 4y^2. If x=y=0 then the answer is NO but if x=4 and y=1 then the answer is YES. Not sufficient.

(2) x > 1. Not sufficient.

(1)+(2)  x = 4y^2  -->  y=\frac{\sqrt{x}}{2}  (or  y=-\frac{\sqrt{x}}{2}=negative ). Now, since  x>1  then  x>\sqrt{x} , so  x>(\frac{\sqrt{x}}{2}=y) . Sufficient.

Answer: C.

AbhiJ · Answer

Thanks Bunuel, could you point to other similar inequalities problems.

Bunuel · Answer

Check below links. DS questions on inequalities: search.php?search_id=tag&tag_id=184 PS questions on inequalities: search.php?search_id=tag&tag_id=64 Hope it helps.

mariofelix · Answer

Hi Bunuel, i got 2 approaches yielding different results. Can you please take a look? 1. Approach x = 4y^2 ; 1 < x => 1 < 4y^2 => 1/4 < y^2 2. Approach x = 4y^2 ; 1 < x => x/x = (4y^2)/x 1 = (4y^2)/x but if 1 < x then (4y^2)/x < x => 4y^2 < 1 => y^2 < 1/4 Where is the flaw ? Thanks in advance

Bunuel · Answer

\frac{(4y^2)}{x} < x  -->  4y^2 < x^2 , not  4y^2 < 1 .

gwu · Answer

easy to eliminate ADB

answer is C

Stat 1: x = 4y^2
Stat 2: x>1

1+2: since x > 1( x^2 is always greater that x) and y^2 is also positive. It follows that lxl = 4ly^2l
hence, x> y

GSBae · Answer

To solve these types of inequality questions, it's useful to see the ranges where x>y, x If x<0 (for instance, -1, then y = 4), xy If x>1/4 (for instance, x = 1, y= 4) x1, we know that it's outside this range and therefore that x

NoHalfMeasures · Answer

Ans C

Please check the solution in the picture attached

stonecold · Answer

For any inequality we must the check the bound (-1,0) and (0,1)
THEY BEHAVE FUNNY WHEN SQUARED....
WRITE THAT DOWN...

AbdurRakib · Answer

(1)  when y= \frac{1}{2} ,then x=4 (\frac{1}{2})^2 =1,so x>Y
  When y= \frac{1}{4} ,then x=4 (\frac{1}{4})^2 = \frac{1}{4} ,x=y, Not Sufficient

(2) No information about y ,Clearly  Not sufficient

(1)+(2) when x>1 ,x is always greater than y in terms of the equation from Statement (1), Sufficient

Correct Answer C

hunk107 · Answer

Is x > y ?

(1) x = 4y^2 ---> It represents the equation of parabola symmetric towards Ist and 4th quadrant , x can be +ve or zero 
 if any +ve value , y> x , for x=0 , x=y=0; ( INSUFF)

(2) x > 1 --- standalone not sufficient

by combining we know that x is value greater than > 1 , and it is always smaller than y

(C) is the answer

abrakadabra21 · Answer

Is x > y ?

(1) x = 4y^2
(2) x > 1

(1) x = 4y^2

if y =0 => x =0 No
if y =1 & x= 4 yes
if y= 1/2 x = 1 yes

(2) x > 1

both combined yes

jkbk1732 · Answer

The highlighted part is incorrect. The variables X & Y are interchanged in the post above. Please find below the corrected form. y = 4y^2 1 = 4y (dividing by y means we have to consider the case when y = 0. Notice in this case that x = y. y = 1/4. So our critical values here are y = 0 and y = 1/4. <-------(0)--------(1/4)--------> If y<0 (for instance,y= -1, then x= 4), x>y if 01, so, x>y.. Both statement sufficient) If y>1/4 (for instance, y = 1, x= 4)x>y So, for x to be greater than y, y has to be greater than 1/4 or less than 0. This is not enough information on its own. Insufficient.

Basshead · Answer

Is  x > y ?

(1)  x = 4y^2

=  \frac{x}{4 }= y^2

=  \frac{\sqrt{x} }{2} = y

x >  \frac{\sqrt{x} }{2}?

We don't know if x = 0. Insufficient.

(2)  x > 1

Clearly insufficient.

(1&2) If x > 1 then:

let x = 2

2 >  \frac{\sqrt{2} }{2}?

True for all scenarios. SUFFICIENT.

Michele4 · Answer

Bunuel chetan2u can we also solve it by putting 4y^2>1, which gives us -1/21 then x>y?

bumpbot · Answer

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Is x > y ? (1) x = 4y^2 (2) x > 1

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