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Bunuel
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Bunuel
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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Sorry guys there was a typo in the source. Fixed it. Thank you.
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Bunuel
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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The equation can be simply rearranged as (x-y) + (x-y)*1/3

Substituting for x-y we get 12

(D)

Posted from my mobile device
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Bunuel
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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Fastest way:

\((x - \frac{y}{3}) - (y - \frac{x}{3}) = (x - y) + \frac{1}{3}(x - y) = 9 + 3 = 12\).
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Bunuel
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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stne ; edited thanks :)
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Bunuel
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.

Answer: D
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