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# The functions f and g are defined as f(x, y) = 2x + y and g

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The functions f and g are defined as f(x, y) = 2x + y and g [#permalink]  14 May 2019, 01:12
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The functions f and g are defined as f(x, y) = 2x + y and g(x, y) = x + 2y.

 Quantity A Quantity B f(3, 4) + g(3, 4) f(4, 3) + g(4, 3)

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The functions f and g are defined as f(x, y) = 2x + y and g [#permalink]  14 May 2019, 08:15
Expert's post
When provided algebra for Quantitative Comparison problems, consider solving algebraically first, because the approach is likely to be more efficient than plugging in.

In this case we have:

 Quantity A Quantity B f(3, 4) + g(3, 4) f(4, 3) + g(4, 3)

Now, in the root statement f(x, y) = 2x + y and g(x + y) = x + 2y | Since both quantities sum these equations, stack and sum the full equations to efficiently compare the quantities.

2x + y
+ x + 2y
3x + 3y

Without plugging in, it can be determined that when adding the two functions of both quantities the x and y coefficients will remain equal. Therefore, since the x and y values are the same in both quantities, the quantities themselves will always be equal, which is choice C.
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Stefan Maisnier

Re: The functions f and g are defined as f(x, y) = 2x + y and g   [#permalink] 14 May 2019, 08:15
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