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

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Joined: 02 Sep 2009
Posts: 55188
Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0  [#permalink]

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26 Apr 2019, 03:27
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Difficulty:

15% (low)

Question Stats:

73% (00:55) correct 27% (01:02) wrong based on 64 sessions

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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

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Posts: 7681
Re: Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0  [#permalink]

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26 Apr 2019, 04:10
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
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Re: Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0  [#permalink]

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27 Apr 2019, 09:37
Top Contributor
Bunuel wrote:
Is x = y ?

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

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

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

Cheers,
Brent
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Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0  [#permalink]

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Updated on: 27 Apr 2019, 11:26
Bunuel wrote:
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

#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
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Originally posted by Archit3110 on 27 Apr 2019, 10:14.
Last edited by Archit3110 on 27 Apr 2019, 11:26, edited 1 time in total.
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Re: Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0  [#permalink]

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27 Apr 2019, 11:24
Archit3110 wrote:
Bunuel wrote:
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

#1
$$\frac{2x}{3} - \frac{y}{3} = \frac{1}{3}$$
2x=y
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
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Re: Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0  [#permalink]

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27 Apr 2019, 11:27
edited thanks
Mo2men

Mo2men wrote:
Archit3110 wrote:
Bunuel wrote:
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

#1
$$\frac{2x}{3} - \frac{y}{3} = \frac{1}{3}$$
2x=y
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

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Re: Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0  [#permalink]

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09 May 2019, 17:24
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

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Re: Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0  [#permalink]

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13 May 2019, 10:34
Bunuel wrote:
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

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

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Re: Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0   [#permalink] 13 May 2019, 10:34
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