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# Which of the following is equivalent to (x+y)/3−(x−y)/4?

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Math Expert
Joined: 02 Sep 2009
Posts: 44599
Which of the following is equivalent to (x+y)/3−(x−y)/4? [#permalink]

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06 Apr 2018, 09:12
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Which of the following is equivalent to $$\frac{x+y}{3}−\frac{x−y}{4}$$?

A. $$\frac{x+y}{12}$$

B. $$\frac{7x+y}{12}$$

C. $$\frac{7x−y}{12}$$

D. $$\frac{7y+x}{12}$$

E. $$\frac{7y−x}{12}$$
[Reveal] Spoiler: OA

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Which of the following is equivalent to (x+y)/3−(x−y)/4? [#permalink]

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06 Apr 2018, 09:19
Bunuel wrote:
Which of the following is equivalent to $$\frac{x+y}{3}−\frac{x−y}{4}$$?

A. $$\frac{x+y}{12}$$

B. $$\frac{7x+y}{12}$$

C. $$\frac{7x−y}{12}$$

D. $$\frac{7y+x}{12}$$

E. $$\frac{7y−x}{12}$$

we are given : (x+y)/3 - (x-y)/4 *** LCM of 3 and 4 is 12.

={4(x+y) - 3(x-y) }/ 12
=(4x+4y-3x+3y) / 12
= x+ 7y / 12

So, the correct answer is D.
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Which of the following is equivalent to (x+y)/3−(x−y)/4? [#permalink]

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06 Apr 2018, 20:05
Bunuel wrote:
Which of the following is equivalent to $$\frac{x+y}{3}−\frac{x−y}{4}$$?

A. $$\frac{x+y}{12}$$

B. $$\frac{7x+y}{12}$$

C. $$\frac{7x−y}{12}$$

D. $$\frac{7y+x}{12}$$

E. $$\frac{7y−x}{12}$$

$$\frac{x+y}{3}−\frac{x−y}{4}$$=

$$(\frac{x+y}{3}*\frac{4}{4}) −(\frac{x−y}{4}*\frac{3}{3})$$

$$\frac{4(x+y)}{3*4} −\frac{3(x−y)}{4*3}=$$

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

(Change the sign of terms being subtracted!)

$$\frac{4x+4y-3x+3y}{12}=$$

=$$\frac{x + 7y}{12}$$

Answer D
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Which of the following is equivalent to (x+y)/3−(x−y)/4?   [#permalink] 06 Apr 2018, 20:05
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# Which of the following is equivalent to (x+y)/3−(x−y)/4?

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