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

Question

Is x > y?

(1) x/4 = y^2

(2) x > 1

Bunuel · Accepted Answer

Is x > y ?

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

Answer: C.

ashish8 · Answer

Simplify 1:
 X = 4Y^2

The squared tells us the right side will always be positive and for integers X will always be greater then Y irrespective if Y is positive or negative.

Y = 1/4 --> X = 1/4.

So now we know we need B to filter the values.

shirisha091 · Answer

Why do you need to know that x>1 to find out that y= sq.root x/2? couldn't you have found that in A?

EvaJager · Answer

(1) Since x=4y^2 , the question becomes whether 4y^2>y , or y(4y-1)>0. We don't know anything about y, so not sufficient. Check for example y = 0 and y = 1 . (2) Obviously not sufficient, as we don't know anything about y . (1) and (2): Since x > 1 , x=4y^2>1 , from which y>1/2 or y<-1/2 . Then x=4y^2>y , because y(4y-1)>0 holds for either y > 1/2 or y < -1/2 . Sufficient. Answer C

CEdward · Answer

Inequalities are tough...I find myself getting into a bad habit of picking numbers - it's so terribly time consuming. Does anyone have any tips for tackling inequalities without doing that so often?

x > y 
St1 - x/4 = y^2 --> x = 4y^2
x = 4, y = 1 YES
x = 0, y = 0 NO
Insufficient.

St2 - x > 1 
Clearly insufficient

Combo pack: x > 1 YES

GMATGuruNY · Answer

Alternate approach: Statement 1: \frac{x}{4} = y^2 x = 4y^2 If y=0 and x=0, then x=y, so the answer to the question stem is NO. If y=1 and x=4, then x>y, so the answer to the question stem is YES. INSUFFICIENT. Statement 2: x > 1 No information about y. INSUFFICIENT. Statements combined: x = 4y^2 and x > 1 Case 1: x=y Substituting x=y into x = 4y^2 , we get: x = 4x^2 1 = 4x x = \frac{1}{4} Not viable, since Statement 2 requires that x > 1. Case 2: x < y , implying that 1 < x < y and that y > 1 Substituting x= 4y^2 into x < y, we get: 4y^2 < y 4y < 1 y < \frac{1}{4} Not viable, since Case 2 requires that y > 1. Since x≤y is not possible, x > y. Thus, the answer to the question stem is YES. SUFFICIENT. C

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

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