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If @ is defined as any function, what is the value of 2020 @ 2019?

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If @ is defined as any function, what is the value of 2020 @ 2019?

by Max@Math Revolution » Mon Jan 13, 2020 12:12 am
[GMAT math practice question]

If @ is defined as any function, what is the value of 2020 @ 2019?

1) For any x and y, x @ y is defined as x - y.
2) For any x, y and z, x @ x is defined as 0 and x @ (y @ z) is defined as (x @ y) + z.
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Source: — Data Sufficiency |
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Re: If @ is defined as any function, what is the value of 2020 @ 2019?

by Max@Math Revolution » Wed Jan 15, 2020 12:18 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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 1 variable (the operation @) and 0 equations, D is most likely the answer. So, we should consider each condition on its own first.

Condition 1)
We have 2020 @ 2019 = 2020 – 2019 = 1.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
If x = y = z, then x @ (x @ x) = x @ 0, x @ (x @ x) = (x @ x) + x = 0 + x = x and x @ 0 = x.
If y = z, then we have x = x @ 0 = x @ (y @ y) = (x @ y) + y and x @ y = x – y.
Thus we have 2020 @ 2019 = 2020 – 2019 = 1.
Since condition 2) yields a unique solution, it is sufficient.


Note: Tip 1) of the VA method states that D is most likely the answer if condition 1) gives the same information as condition 2).

Therefore, D is the answer.
Answer: D

This question is a CMT 4(B) question: condition 1) is easy to work with, and condition 2) is difficult to work with. For CMT 4(B) questions, D is most likely the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations,” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C, or E.
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