Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0 GMAT Data Sufficiency

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

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2018". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:
The question is to check whether x equals y:
Statement 1: \(\frac{2x}{3} - \frac{y}{3}= \frac{1}{3}\)
Multiply both sides by 3 to get:
2x−y=1
which implies y=2x−1
There can be different values of x and y which satisfy y=2x−1.
Case i: x = 1 and y = 1. Here, we can see that it fulfills the condition. So x equals y.
Case ii: x = 3 and y = 5. Here, we can see that it does not fulfill the condition. Thus x does not equal y
Hence, it can be seen that statement 1 is not sufficient.
Statement 2:\(\frac{x}{4} - \frac{x}{4}= 0\)
Multiply both sides by 4 to get:
x−y=0
which implies x=y
This shows that statement 2 satisfies the equation. Hence, statement 2 is Sufficient.
Correct Answer: B

Approach Solution 2:
We need to determine whether x = y.
Statement One Alone:
\(\frac{2x}{3} - \frac{y}{3}= \frac{1}{3}\)
Multiplying both sides by 3, we have
2x - y = 1
implies 2x = y + 1
This equation is not sufficient alone to satisfy the equation. We can further consider,
if x = 1 and y = 1, then x = y. However, if x = 2 and y = 3, then x ≠ y. Therefore statement one alone is not sufficient.
Statement Two Alone:
\(\frac{x}{4} - \frac{x}{4}= 0\)
Multiplying both sides by 4, we have
x - y = 0
implies x = y
Here we can see that statement 2 alone is sufficient.
Correct Answer: B

Approach Solution 3:

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

Correct Answer: B

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