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f(x) = anx^n + an-1x^{n-1} + … + a1x + a0. What is the sum

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by Max@Math Revolution » Tue May 28, 2019 12:42 am

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A

B

C

D

E

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[GMAT math practice question]

f(x) = anx^n + an-1x^{n-1} + ... + a1x + a0. What is the sum of the coefficients of the function f?

1) f(1) = 20
2) f(-1) = 10
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu May 30, 2019 12:11 am
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

f(1) = an*1^n + an-1*1^{n-1} + ... + a1*1 + a0 = an + an-1 + ... + a1 + a0 , which is the sum of all coefficients of f(x).
Thus, condition 1) is sufficient, because it is equivalent to the question.

Therefore, A is the answer.
Answer: A
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