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What is the value of [x] + [-x]? ([x] means the greatest integer less than o

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What is the value of [x] + [-x]? ([x] means the greatest integer less than o

by Max@Math Revolution » Wed Feb 05, 2020 2:00 am
[GMAT math practice question]

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

1) 0 ≤ x.
2) x is not an integer.
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Source: — Data Sufficiency |
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Re: What is the value of [x] + [-x]? ([x] means the greatest integer less than o

by Max@Math Revolution » Fri Feb 07, 2020 1:05 am
=>


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.

If x = n + h where n is an integer and 0 ≤ h < 1, then [x] = n. Here n is the integer part of n, and h is the decimal part of n.

If x is an integer, then we have x = n + h where h = 0, [x] = n, [-x] = -n and [x] + [-x] = n + (-n) = 0.

Assume x is not an integer.
Then we have x = n + h where 0 < h < 1, [x] = n.
We have -x = -n - h, -x = -n - 1 + 1 - h, -x = -(n + 1) + (1 - h) where 0 < 1 - h < 1.
Thus [-x] = -n - 1 and we have [x] + [-x] = n + (-n - 1) = -1.

Condition 2) tells us that x is not an integer. Therefore [x] + [-x] = -1 and condition 2) yields a unique solution.

Condition 2) is sufficient.

Condition 1)
If x = 0 which is an integer, then we have [x] + [-x] = 0.
If x = 1.5 which is not an integer, then we have [x] + [-x] = -1.

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

Therefore, B is the answer.
Answer: B
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Re: What is the value of [x] + [-x]? ([x] means the greatest integer less than o

by deloitte247 » Sat Feb 08, 2020 12:45 am
We need to find the value of x before applying the function [x] which is the greatest integer that is less than or equal to x before evaluation [x +[ - x ]

Statement 1 => $$0\le x$$
This means x can be any number between 0 and infinity and [x] can be the greatest integer that is less than or equal to any number in the range $$0\le x<\inf inity$$
Since the value of x remains unknown, statement 1 is NOT SUFFICIENT

Statement 2 => x is not an integer
The only information we have about x is that it might be a fraction/decimal and this does not give the value oh x. hence, statement 2 is NOT SUFFICIENT

Combining both statements together =>
$$0\le x$$ and x is not an integer. This means x can be any decimal number/fraction between 0 and infinity since the value of x is still unknown.
Both statements together ARE NOT SUFFICIENT
Answer = option E
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