Is x y? (1) x^2 y (2) √x

Question

Is x > y?

(1) x^2 > y 
(2) √x < y

Bunuel · Answer

Is x > y?

(1) x^2 > y. Clearly insufficient: if x=2 and y=3 then the answer is NO but if x=2 and y=1 then the answer is YES.

(2) √x < y. Also insufficient: if x=4 and y=5 then the answer is NO but if x=4 and y=3 then the answer is YES. Notice that since x is under the square root sign then it must be true that \(x\geq{0}\).

(1)+(2) \(\sqrt{x}<y<x^2\) --> both \(x\) and \(y\) are between \(\sqrt{x}\) and \(x^2\), but we can not say which one is greater. Not sufficient. For example: if \(x=y=4\) (\(\sqrt{4}<4<4^2\)) then the answer is NO but if \(x=4\) and \(y=3\) (\(\sqrt{4}<3<4^2\)) then the answer is YES. Not sufficient.

Answer: E.

Hope it's clear.

GMATPASSION · Answer

Its not always possible to take examples like you have shown for each statement. I mean sometimes the variable values just doesn't fit. Solving it by use of abstract maths is tough.

Ho do we tackle this situation. Do we have a strategy on how to pick numbers faster for testing.

Bunuel · Answer

First of all: on DS questions when plugging numbers, goal is to prove that the statement is not sufficient . So we should try to get a YES answer with one chosen number(s) and a NO with another. Now, number picking strategy can vary for different problems. Generally it's good to test negative/positive/zero as well as integer/fraction to get a YES and a NO answers. If you deal with two variables it's also helpful to test xy in addition to the former. As for this question: you don't really need to test the numbers for it, I just used them to demonstrate that the statements are not sufficient. From (1)+(2): we have that \sqrt{x}1 ): \sqrt{x} ------ x ------ x^2 , now y can be in the green range (answer YES) as well in the red range (answer NO). So, we can not say whether x>y. Hope it's clear.

hfbamafan · Answer

1) Statement 1 only tells us that x is positive and nothing else. So insufficient 2) Statement 2 wants us to go through the process of squaring both sides to make the equation x y and combined, xy^2 x^2 > y

EvaJager · Answer

Is x > y? (1) x^2 > y (2) √x < y E Can anyone explain a simple method to this could not follovv statement B (1) For x=-2 > y=-3, \, x^2=4>-3. But x=2 < y=3 , although x^2=4>y=3. Not sufficient. (2) From the given inequality it follows that x must be non-negative (because of the square root) and since y>\sqrt{x}\geq0 , necessarily y is positive. Therefore, we can square the given inequality and get xy. But if y=1, we cannot have simultaneously xy=1. Not sufficient. (1) and (2) together: Consider the two cases: x=2, y=3 and x=4,y=3. Again, not sufficient. Answer E.

EvaJager · Answer

(2) We know about the signs:  x  must be non-negative, otherwise the square root is not defined. Also, because the square root is non-negative,  y  must be positive. Therefore, in this case we can square the given inequality and obtain  x<y^2.

abhi398 · Answer

statement 2: in Gmat.... sqrt(x) means x is always positive .... therefore from statement 2 we know x is a positive number.

from statement 1 : x*x=y ..insufficient because we x and y can have any values....

combining 1 and 2:
sqrt(x) < y < x*x .... not possible to determine whether x> y

KrishnanTN · Answer

Hi Bunuel,

Pls can you tell us how we can conclude that x > 1 because  \sqrt{x}  <  x^2  please ?

Thanks
Krishnan

Bunuel · Answer

\sqrt{x}<x^2 ;

Square:  x < x^4 :

Reduce by x:  1 < x^3 . Here we know that x > 0 (because if x were negative  \sqrt{x}  would not be defined), so we can safely reduce by x.

Take the cube root:  1 < x .

KrishnanTN · Answer

I take it that the we are eliminating the case where x = 0, because  \sqrt{x}  cannot be lesser than x^2 if x were to be equal to 0.

KrishnanTN · Answer

Hi  Bunuel ,

Is the following solution correct please ?
 Is x >y ?

1) x^2 > y - This is a parabola, symmetrical around the y axis. 
juxtapose the parabola and the straight line. Not sufficient.

2) x^.5 ,y - A half parabola. Juxtapose x=y and this. Not sufficient.

1 + 2 --> THese 3 curves still cannot answer the question.
Is this approach okay please ?

CapnSal · Answer

Can this be a logically correct approach?

Statement 1 and Statement 2: Insufficient

Together:

Subtract the equations:
X^2 - Y^2 > Y - X
(X + Y) (X - Y) > -(-Y+X)
=>X+Y>-1. Cannot create X-Y>0 from this combination therefore insufficient.
Ans E

OmkarSheth008 · Answer

I cam across the same question but in statement B the option is ( root of x is > y ) 
and the answer mentioned is option c :- both statement together sufficient

Bunuel  can you please explain this question with the above mentioned context

Bunuel · Answer

That question is discussed here: https://gmatclub.com/forum/is-x-y-1-x-2 ... 80724.html

bumpbot · Answer

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Is x > y? (1) x^2 > y (2) √x < y

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