Which of the following is equivalent to $$\frac{x+y}{3}-\frac{x-y}{4}?$$
$$A.\ \frac{x+y}{12}$$
$$B.\ \frac{7x+y}{12}$$
$$C.\ \frac{7x-y}{12}$$
$$D.\ \frac{7y+x}{12}$$
$$E.\ \frac{7y-x}{12}$$
[spoiler]OA=D[/spoiler]
Source: Veritas Prep
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Which of the following is equivalent to
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GMATGuruNY
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Let x=2 and y=1, with the result that (x+y)/3 - (x-y)/4 = 1 - 1/4 = 3/4.M7MBA wrote:Which of the following is equivalent to $$\frac{x+y}{3}-\frac{x-y}{4}?$$
$$A.\ \frac{x+y}{12}$$
$$B.\ \frac{7x+y}{12}$$
$$C.\ \frac{7x-y}{12}$$
$$D.\ \frac{7y+x}{12}$$
$$E.\ \frac{7y-x}{12}$$
The correct answer must yield 3/4 when x=2 and y=1.
Only D works:
(7y+x)/12 = (7*1 + 2)/12 = 9/12 = 3/4
The correct answer is D.
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Brent@GMATPrepNow
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Here's another approach....M7MBA wrote:Which of the following is equivalent to $$\frac{x+y}{3}-\frac{x-y}{4}?$$
$$A.\ \frac{x+y}{12}$$
$$B.\ \frac{7x+y}{12}$$
$$C.\ \frac{7x-y}{12}$$
$$D.\ \frac{7y+x}{12}$$
$$E.\ \frac{7y-x}{12}$$
[spoiler]OA=D[/spoiler]
Source: Veritas Prep
Take: $$\frac{x+y}{3}-\frac{x-y}{4}$$
Find common denominator: $$\frac{4(x+y)}{12}-\frac{3(x-y)}{12}$$
Expand numerators: $$\frac{4x+4y}{12}-\frac{3x-3y)}{12}$$
Combine fractions: $$\frac{(4x+4y)-(3x-3y)}{12}$$
Simplify numerator: $$\frac{x+7y}{12}$$
Answer: D
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Brent
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Scott@TargetTestPrep
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Getting an LCD of 12, we have:M7MBA wrote:Which of the following is equivalent to $$\frac{x+y}{3}-\frac{x-y}{4}?$$
$$A.\ \frac{x+y}{12}$$
$$B.\ \frac{7x+y}{12}$$
$$C.\ \frac{7x-y}{12}$$
$$D.\ \frac{7y+x}{12}$$
$$E.\ \frac{7y-x}{12}$$
[spoiler]OA=D[/spoiler]
Source: Veritas Prep
(4x + 4y)/12 - (3x - 3y)/12
(x + 7y)/12
Answer: D
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