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f(x) ã…‡ f(y) is defined as f(x+y+2xy). What is the value of

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f(x) ã…‡ f(y) is defined as f(x+y+2xy). What is the value of

by Max@Math Revolution » Tue Oct 01, 2019 11:43 pm
[GMAT math practice question]

f(x) ã…‡ f(y) is defined as f(x+y+2xy). What is the value of 1 ã…‡ (-1)?

1) f(-1)=-1 and f(0)=1
2) f(x)=2x+1
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Oct 03, 2019 11:22 pm
=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have many variables to determine a function and 0 equations, E is most likely to be the answer. However, by Tip 1) of the VA method, D is most likely to be the answer if condition 1) gives the same information as condition 2).

Condition 1)
1 ã…‡ (-1) = f(0) ã…‡ f(-1)=f(0+(-1)+0)=f(-1)=-1.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since we have f(0)=1 and f(-1)=-1, we have 1 ã…‡ (-1) = f(0) ã…‡ f(-1)=f(0+(-1)+0)=f(-1)=-1.
Since condition 2) yields a unique solution, it is sufficient.

Therefore, D is the answer.
Answer: D
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