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What is the value of y?

Expert replies
by akhilsuhag » Wed Jun 04, 2014 11:22 am
If x and y are positive, what is the value of y?

(1) xy is the square of an integer.

(2) 600 percent of x equals 200 percent of y.
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Source: — Data Sufficiency |

by GMATGuruNY » Wed Jun 04, 2014 12:03 pm
akhilsuhag wrote:If x and y are positive, what is the value of y?

(1) xy is the square of an integer.

(2) 600 percent of x equals 200 percent of y.
Statement 1: xy is the square of an integer
Let xy = 1² = 1.
It's possible that x=1 and y=1.
It's possible that x=2 and y=1/2.
Since y can be different values, INSUFFICIENT.

Statement 2: 600 percent of x equals 200 percent of y.
(600/100)x = (200/100)y
6x = 2y
3x = y.
It's possible that x=1 and y=3.
It's possible that x=2 and y=6.
Since y can be different values, INSUFFICIENT.

Statements combined:
Case 1: xy = 1² = 1
Substituting y=3x into xy = 1, we get:
(x)(3x) = 1
x² = 1/3
x = √(1/3).
In this case, y = 3x = 3√(1/3).

Case 2: xy= 2² = 4
Substituting y=3x into xy = 4, we get:
(x)(3x) = 4
x² = 4/3
x = √(4/3).
In this case, y = 3x = 3√(4/3).

Since y can be different values, INSUFFICIENT.

The correct answer is E.
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by Brent@GMATPrepNow » Wed Jun 04, 2014 12:11 pm
akhilsuhag wrote:If x and y are positive, what is the value of y?

(1) xy is the square of an integer.
(2) 600 percent of x equals 200 percent of y.
Target question: What is the value of y?

Given: x and y are positive

Statement 1: xy is the square of an integer.
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 1. Here xy = (1)(1) = 1, which is the square of an integer. In this case y = 1
Case b: x = 2 and y = 2. Here xy = (2)(2) = 4, which is the square of an integer. In this case y = 2
Since we cannot answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 600 percent of x equals 200 percent of y.
So, 6x = 2y
Divide both sides by 2 to get: 3x = y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 3. In this case y = 3
Case a: x = 2 and y = 6. In this case y = 6
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that xy is the square of an integer.
Statement 2 tells us that 3x = y
Take statement 1 and replace y with 3x to get: x(3x) is the square of an integer.
In other words, 3x² is the square of an integer.
There are several values of x that satisfy this condition. Here are two:
Case a: x = √3. This means 3x² = 3(√3)² = 9, and 9 is the square of an integer. From statement 2, if x = √3, then y = 3√3.
Case b: x = 4√3. This means 3x² = 3(4√3)² = 36, and 36 is the square of an integer. From statement 2, if x = 4√3, then y = 12√3.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
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