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

Question

Is x = y ?

(1)  \frac{2x}{3} - \frac{y}{3} = \frac{1}{3}

(2)  \frac{x}{4} - \frac{y}{4} = 0

DS45530.01
OG2020 NEW QUESTION

chetan2u · Answer

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

BrentGMATPrepNow · Answer

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

EMPOWERgmatRichC · Answer

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

GMAT assassins aren't born, they're made, 
Rich

ZoltanBP · Answer

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

Cee18 · Answer

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?

chetan2u · Answer

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

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=BLzVLy7rswg

ScottTargetTestPrep · Answer

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

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=7A4C1-Iz0Rg

bumpbot · Answer

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

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

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