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If the symbol # represents one of addition, subtraction, mul

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by Max@Math Revolution » Fri Jun 07, 2019 12:52 am

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Answers

A

B

C

D

E

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[GMAT math practice question]

If the symbol # represents one of addition, subtraction, multiplication, or division, what is the value of (2 # 1)?

1) 2 # 2 = 1
2) (-1/2) # (-1) = 1/2
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Jun 09, 2019 5:08 pm
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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.

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

Condition 1)
# is the division operation since 2 / 2 = 1.
So, 2#1 = 2/1 = 2.
Condition 1) is sufficient since it yields a unique answer.

Condition 2)
# could be the multiplication, subtraction or the division operation
since (-1/2) * (-1) = 1/2, (-1/2)-(-1) = (1/2) and (-1/2)/(-1) = 1/2.

Since 2 * 1 = 2 and 2 / 1 = 2, but 2-1 = 1, condition 2) does not yield a unique value for 2#1.
Condition 2) is not sufficient since it doesn't yield a unique answer.

Therefore, A is the answer.
Answer: A

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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