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<x> is the largest integer less than or equal to x and

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by Max@Math Revolution » Tue Jul 17, 2018 12:03 am

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[GMAT math practice question]

< x > is the largest integer less than or equal to x and [x] is the smallest integer greater than or equal to x. If x is not an integer, which of the following could be the value of [x] - < x >?

A. 1
B. 2
C. 3
D. 4
E. 5
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by GMATGuruNY » Tue Jul 17, 2018 3:11 am
Max@Math Revolution wrote:[GMAT math practice question]

< x > is the largest integer less than or equal to x and [x] is the smallest integer greater than or equal to x. If x is not an integer, which of the following could be the value of [x] - < x >?

A. 1
B. 2
C. 3
D. 4
E. 5
Let x = 0.5.
< x > = <0.5> = the largest integer less than 0.5 = 0.
[x] = [0.5] = the smallest integer greater than 0.5 = 1.
[x] - < x > = 1 - 0 = 1.

The correct answer is A.
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by swerve » Wed Jul 18, 2018 12:22 pm
Let x = 0.5
<x> = <0.5> = the largest integer less than 0.5 = 0.

[x] = [0.5] = the samllest integer greater than 0.5 = 1.

[x] - <x> = 1 - 0 = 1.

Hence, A is the correct answer.
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by Max@Math Revolution » Thu Jul 19, 2018 12:46 am
=>

< x > can be defined in the following way:
If m ≤ x < m + 1, where m is an integer, then < x > = m.

[x] can be defined in the following way:
If n - 1 < x ≤ n, where n is an integer, then [x] = n.

Since x is not an integer, there is an integer n such that n - 1 < x < n.
So, < x > = n -1 and [x] = n.
Thus, [x] - < x > = n - ( n - 1 ) = 1.

We can also solve this problem by plugging in numbers. If x = 1.1, then
[1.1] - <1.1> = 2 - 1 = 1.

Therefore, the answer is A.

Answer: A
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by Scott@TargetTestPrep » Thu Jul 19, 2018 4:22 pm
Max@Math Revolution wrote:[GMAT math practice question]

< x > is the largest integer less than or equal to x and [x] is the smallest integer greater than or equal to x. If x is not an integer, which of the following could be the value of [x] - < x >?

A. 1
B. 2
C. 3
D. 4
E. 5
We can let x = 1.5, so [x] = 2 and <x> = 1. Therefore, [x] - <x> = 2 - 1 = 1.

Answer: A

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