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

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.
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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.

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?

(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
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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
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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.


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