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When x is a real number

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When x is a real number

by Max@Math Revolution » Thu Mar 05, 2020 2:17 am

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[GMAT math practice question]
When x is a real number, {x} denotes the integer part of \(\sqrt{x}\) and [x] the decimal part of \(\sqrt{x}\) . What is the value of x?

1) {x} = 2
2) 0.3 < [x] < 0.5
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Source: — Data Sufficiency |
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Re: When x is a real number

by Max@Math Revolution » Sun Mar 08, 2020 6:18 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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

We have x = {x} + [x] since {x} is the integer part of x and [x] is the decimal part of x.

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

Condition 1)
{x} = 2 means we have 2 ≤ x < 3.

Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)

0.3 < [x] < 0.5 means that we have 0.3 < x < 0.5, 1.3 < x < 1.5, … .

Since condition 2) does not yield a unique solution, it is not sufficient.

Conditions 1) & 2)
Since 0.3 < [x] < 0.5 and {x} = 2, we have 2.3 < {x} + [x] < 2.5.
Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

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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