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What is the value of [x]/(x - [x]) - x/([-x + 1] + x)? ([x] means the greatest integer less

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What is the value of [x]/(x - [x]) - x/([-x + 1] + x)? ([x] means the greatest integer less

by Max@Math Revolution » Fri Jan 31, 2020 1:43 am
[GMAT math practice question]

What is the value of [x]/(x - [x]) - x/([-x + 1] + x)? ([x] means the greatest integer less than or equal to x)

1) 2 ≤ x < 3.
2) x is not integer.
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Source: — Data Sufficiency |
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Re: What is the value of [x]/(x - [x]) - x/([-x + 1] + x)? ([x] means the greatest integer less

by Max@Math Revolution » Sun Feb 02, 2020 6:21 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.
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Since we have 1 variable (x) and 0 equations, D is most likely the answer. So, we should consider each condition on its own first.

Condition 1)
Since 2 ≤ x < 3, we have [x]/(x - [x]) - x/([-x + 1] + x) = 2/(x - 2) - x/(-2+ x) = (2 - x)/(x - 2) = -1(x - 2)/(x - 2) = -1.

Since condition 1) yields a unique solution, it is sufficient.

Condition 2) If x = n + h where n is the integer part of x and h is the positive decimal part of x, then we have:
[x]/(x - [x]) - x/([-x + 1] + x) = n/h - (n + h)/(-n + n + h) = n/h - (n + h)/h = -h/h = -1.

Since condition 2) yields a unique solution, it is sufficient.

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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