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

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MathRevolution
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<x> is the largest integer less than or equal to x and [x] is the smal [#permalink] New post   17 Jul 2018, 01:12
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5% (low)

Question Stats:

92% (01:14) correct 8% (01:09) wrong based on 75 sessions
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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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A
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<x> is the largest integer less than or equal to x and [x] is the smal [#permalink] New post   17 Jul 2018, 01:18
MathRevolution 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 \(x=I.abc\), where \(I,a,b,c\) are some numbers

Given \(<x>=I\) and \([x]=I+1\)

Therefore \([x]-<x>=I+1-I=1\)

Option A
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Re: <x> is the largest integer less than or equal to x and [x] is the smal [#permalink] New post   17 Jul 2018, 04:04
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MathRevolution 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.

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Re: <x> is the largest integer less than or equal to x and [x] is the smal [#permalink] New post   17 Jul 2018, 04:29
<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

Pick a number 5.6

[x] - <x>
= 6 - 5
= 1

(A)
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Re: <x> is the largest integer less than or equal to x and [x] is the smal [#permalink] New post   19 Jul 2018, 02:28
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=>

<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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Re: <x> is the largest integer less than or equal to x and [x] is the smal [#permalink] New post   19 Jul 2018, 05:27
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Solution



Given:

    • <x> is the largest integer less than or equal to x
    • [x] is the smallest integer greater than or equal to x

Approach and Working:

Let’s suppose x= n.abc, then:
    • <x>= n
    • [x]= n+1
      o Thus, [x] - <x>= 1

Hence, the correct answer is option A.

Answer: A
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Re: <x> is the largest integer less than or equal to x and [x] is the smal [#permalink]
19 Jul 2018, 05:27
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