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a, b, c, d and e are real numbers with a < b < c <

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a, b, c, d and e are real numbers with a < b < c <

by Max@Math Revolution » Thu May 02, 2019 1:20 am

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[GMAT math practice question]
a, b, c, d and e are real numbers with a < b < c < d < e. Is abcde negative?

1) abc < 0
2) cde < 0
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Source: — Data Sufficiency |
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by Max@Math Revolution » Mon May 06, 2019 1:16 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.

Since we have 5 variables and 4 equations, D is most likely to be the answer. So, we should consider each condition on its own first. If a question is an inequality, then inequalities in the original condition can be counted as equations.

Condition 1)
If a = -1, b = 1, c = 2, d = 3, e = 4, then abcde < 0, and the answer is 'yes'
If a = -4, b = -3, c = -2, d = -1, e = 1, then abcde > 0, and the answer is 'no'.
Condition 1) is not sufficient since it doesn't yield a unique answer.

Condition 2)
There are two cases to consider:
i) 0 lies between c and d
ii) 0 is greater than e.
If 0 lies between c and d, then abcde < 0 and the answer is 'yes'.
If 0 is greater than e, then abcde < 0 and the answer is 'yes'.
Condition 2) is sufficient since it gives a unique answer.

Therefore, B is the answer.
Answer: B

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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