Video solution from Quant Reasoning:

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Is x = y ?


(1) \(\frac{2x}{3} - \frac{y}{3} = \frac{1}{3}\)
Multiply the entire equation by 3, so 2x-y=1..
If x=y=1, ans is yes. But, if y=3, x=2, answer is no.
Insuff

(2) \(\frac{x}{4} - \frac{y}{4} = 0\)
Multiply the entire equation by 4, so x-y=0....x=y
Suff

B

Target question: Is x = y?

Statement 1: \(\frac{2x}{3} - \frac{y}{3} = \frac{1}{3}\)
Multiply both sides by 3 to get: \(2x - y = 1\)
Rewrite as: \(y = 2x - 1\)

There are several values of x and y that satisfy the above equation. Here are two:
Case a: x = 1 and y = 1. In this case, the answer to the target question is YES, x EQUALS y
Case b: x = 3 and y = 5. In this case, the answer to the target question is NO, x does NO equal y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: \(\frac{x}{4} - \frac{y}{4} = 0\)
Multiply both sides by 4 to get: \(x - y = 0\)
Add y to both sides to get: \(x = y\)
PERFECT! The answer to the target question is YES, x EQUALS y
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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#1
\(\frac{2x}{3} - \frac{y}{3} = \frac{1}{3}\)
2x=y+1
insufficient
#2
\(\frac{x}{4} - \frac{y}{4} = 0\)

x=y
sufficient
IMO B

I think there is a typo. It must be 2x = y + 1

edited thanks
Mo2men

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:

GMAT assassins aren't born, they're made,
Rich
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The original question: Is \(x=y\) ?

1) We know that \(2x-y=1 \implies y=2x-1\) and can use this statement information to further rephrase the original question.

Is \(x=2x-1\)

\(x=1\) ?

Since \(x\) can be any real number, we can't get a definite answer to the further rephrased question. \(\implies\) Insufficient

2) We know that \(x-y=0 \implies x=y\). Thus, the answer to the original question is a definite Yes. \(\implies\) Sufficient

Answer: B
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Is x = y ?


(1) 2x3−y3=132x3−y3=13
We will not get anything further
Insuff

(2) x4−y4=0x4−y4=0
Suff x/4=y/4
implies x=y

Hi Brent,

re: equation 1, I get why the statement is insufficient because of multiple value. However, I have a counter question. We are wanting to answer if x=y. In statement 1, we know that 2x-1 = y, therefore, x is not equal to y. Since the answer is No, is it not sufficient to answer the target question, i,e: a definitive no that x is not equal to y because y=2x-1. I hope that explanation makes sense. Essentially, what I am trying to get here is that having a "no" answer to the statement is also an accepted answer for the target question?

2x-1=y....
When x=1, y=2*1-1=2-1=1, so x=y=1.....Yes x=y
But for other values say x can be 2, y can be 20....No

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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Answer: Option B

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