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Is x = y?

by AbeNeedsAnswers » Wed May 08, 2019 7:48 pm

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Is x = y?

(1) 2x/3 - y/3 = 1/3
(2) x/4 - y/4 = 0

B

Source: Official Guide 2020

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by [email protected] » Thu May 09, 2019 6:25 am

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AbeNeedsAnswers wrote:Is x = y?

(1) 2x/3 - y/3 = 1/3
(2) x/4 - y/4 = 0
Target question: Is x = y?

Statement 1: 2x/3 - y/3 = 1/3
Multiply both sides by 3 to get: 2x - y = 1
There are several values of x and y that satisfy this equation. Here are two:
Case a: x = 1 and y = 1. In this case, the answer to the target question is YES, it is the case that x = y
Case b: x = 2 and y = 3. In this case, the answer to the target question is NO, it is not the case that x = y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x/4 - y/4 = 0
Multiply both sides by 4 to get: x - y = 0
Add y to both sides to get: x = y
The answer to the target question is YES, it is the case that x = y
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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by [email protected] » Thu May 09, 2019 3:48 pm

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Hi All,

We're asked if X = Y. This is a YES/NO question can be solved with a mix of Arithmetic and TESTing VALUES.

1) (2X/3) - (Y/3) = 1/3

Since each value in this equation is divided by 3, we can 'simplify' the equation by multiplying each term by 3. This gives us:
2X - Y = 1
2X = Y + 1

IF....
X=1 and Y= 1, then the answer to the question is YES.
X=1.5 and Y= 2, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) (X/4) - (Y/4) = 0

Since each value in this equation is divided by 4, we can 'simplify' the equation by multiplying each term by 4. This gives us:
X - Y = 0
X = Y
The information in Fact 2 tells us that X and Y are EQUAL, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

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Re: Is x = y?

by [email protected] » Fri May 14, 2021 6:01 am

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AbeNeedsAnswers wrote:
Wed May 08, 2019 7:48 pm
Is x = y?

(1) 2x/3 - y/3 = 1/3
(2) x/4 - y/4 = 0

B

Source: Official Guide 2020
Solution:

Question Stem Analysis:


We need to determine whether x = y.

Statement One Alone:

Multiplying the equation by 3, we have:

2x - y = 1

2x = y + 1

This does not allow us to determine whether x = y. For example, if x = 1 and y = 1, then x = y. However, if x = 2 and y = 3, then x ≠ y. Statement one alone is not sufficient.

Statement Two Alone:

Multiplying the equation by 4, we have:

x - y = 0

x = y

We see that x is indeed equal to y. Statement two alone is sufficient.

Answer: B

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