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Math Expert V
Joined: 02 Sep 2009
Posts: 58353
If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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Difficulty:   15% (low)

Question Stats: 83% (01:30) correct 17% (02:09) wrong based on 63 sessions

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If x – y = 9, then $$(x - \frac{y}{3}) - (y - \frac{x}{3}) =$$

(A) –4
(B) –3
(C) 0
(D) 12
(E) 27

Source: Nova GMAT
Difficulty Level: 550

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Originally posted by Bunuel on 10 Apr 2019, 21:41.
Last edited by SajjadAhmad on 08 Jul 2019, 00:19, edited 1 time in total.
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Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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Bunuel wrote:
If x – y = 9, then $$(x - \frac{y}{3})(y - \frac{x}{3}) =$$

(A) –4
(B) –3
(C) 0
(D) 12
(E) 27

solve the expression we get
4*(x-y)/3
given x-y= 9
so we get 4*3 = 12
IMO D

Originally posted by Archit3110 on 11 Apr 2019, 00:41.
Last edited by Archit3110 on 15 Apr 2019, 07:19, edited 2 times in total.
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Joined: 12 Sep 2017
Posts: 301
Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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Archit3110

Haha I was trying for 30 minutes and gave up, then I scrolled down and saw your answer, and if you couldn't do it then that it is actually a difficult question xD.

Which was your approach?
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Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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Bunuel wrote:
If x – y = 9, then $$(x - \frac{y}{3})(y - \frac{x}{3}) =$$

(A) –4
(B) –3
(C) 0
(D) 12
(E) 27

This is definitely not a 600 level question. Can some expert or Sir Bunuel provide an approach for this.
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Math Expert V
Joined: 02 Sep 2009
Posts: 58353
Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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Sorry guys there was a typo in the source. Fixed it. Thank you.
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Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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1
Bunuel wrote:
If x – y = 9, then $$(x - \frac{y}{3}) - (y - \frac{x}{3}) =$$

(A) –4
(B) –3
(C) 0
(D) 12
(E) 27

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

$$\frac{{3x - y - 3y + x}}{3}$$

$$\frac{{4x - 4y}}{3}$$

$$\frac{{4(x - y)}}{3}$$

$$\frac{4 * 9}{3}$$

$$12$$ (D)
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Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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The equation can be simply rearranged as (x-y) + (x-y)*1/3

Substituting for x-y we get 12

(D)

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Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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Bunuel wrote:
If x – y = 9, then $$(x - \frac{y}{3}) - (y - \frac{x}{3}) =$$

(A) –4
(B) –3
(C) 0
(D) 12
(E) 27

$$(x-\frac{y}{3})-(y-\frac{x}{3})=\frac{4x}{3}-\frac{4y}{3}=\frac{4*(x-y)}{3}=\frac{4*9}{3}=12$$

IMO, option D>
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Manager  G
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Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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Fastest way:

$$(x - \frac{y}{3}) - (y - \frac{x}{3}) = (x - y) + \frac{1}{3}(x - y) = 9 + 3 = 12$$.
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Director  V
Joined: 27 May 2012
Posts: 902
Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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Archit3110 wrote:
Bunuel wrote:
If x – y = 9, then $$(x - \frac{y}{3})(y - \frac{x}{3}) =$$

(A) –4
(B) –3
(C) 0
(D) 12
(E) 27

solve the expression we get
4*(x-y)/3
given x-y= 3
so we get 4*3 = 12
IMO D

Just a small correction required here x-y =9.
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Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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stne ; edited thanks Target Test Prep Representative D
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Re: If x – y = 9, then (x - y/3) - (y - x/3) =  [#permalink]

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Bunuel wrote:
If x – y = 9, then $$(x - \frac{y}{3}) - (y - \frac{x}{3}) =$$

(A) –4
(B) –3
(C) 0
(D) 12
(E) 27

Simplifying, we have:

3x/3 - y/3 - 3y/3 + x/3

(4x - 4y)/3

4(x - y)/3

Since x - y = 9, we have 4(9)/3 = 12.

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