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# [x] is the greatest integer less than or equal to x. Find the number

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Joined: 20 Jul 2017
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[x] is the greatest integer less than or equal to x. Find the number  [#permalink]

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Updated on: 30 Jun 2019, 21:14
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Difficulty:

65% (hard)

Question Stats:

31% (02:11) correct 69% (02:27) wrong based on 29 sessions

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[x] is the greatest integer less than or equal to x. Find the number of positive integers n such that [$$\frac{n}{7}$$] = [$$\frac{n}{9}$$]

A. 12
B. 13
C. 14
D. 15
E. 16

Originally posted by Dillesh4096 on 30 Jun 2019, 00:47.
Last edited by Dillesh4096 on 30 Jun 2019, 21:14, edited 1 time in total.
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Location: India
Re: [x] is the greatest integer less than or equal to x. Find the number  [#permalink]

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30 Jun 2019, 02:02
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1
When 1≤n≤6, [n/7]=[n/9]=0
When 9≤n≤13, [n/7]=[n/9]=1
When 18≤n≤20, [n/7]=[n/9]=2
When n=27, [n/7]=[n/9]=3

Total possible value of n= 6+5+3+1=15

Dillesh4096 wrote:
[x] is the greatest integer less than or equal to x. Find the number of positive integers n such that [$$\frac{n}{7}$$] = [$$\frac{n}{9}$$]

A. 12
B. 13
C. 14
D. 15
E. 16
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Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10533
Location: United States (CA)
Re: [x] is the greatest integer less than or equal to x. Find the number  [#permalink]

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02 Jul 2019, 17:48
1
1
Dillesh4096 wrote:
[x] is the greatest integer less than or equal to x. Find the number of positive integers n such that [$$\frac{n}{7}$$] = [$$\frac{n}{9}$$]

A. 12
B. 13
C. 14
D. 15
E. 16

We see that when n is any integer from 1 to 6, inclusive, then [n/7] = 0 = [n/9]. Similarly, when n is any integer from 9 to 13, inclusive, then [n/7] = 1 = [n/9]; when n is any integer from 18 to 20, inclusive, then [n/7] = 2 = [n/9]; and lastly, when n = 27, [n/7] = 3 = [n/9].

Therefore, there are 6 + 5 + 3 + 1 = 15 integer values for n.

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Re: [x] is the greatest integer less than or equal to x. Find the number  [#permalink]

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01 Jul 2019, 08:46
Hi, can someone explain the problem?
Re: [x] is the greatest integer less than or equal to x. Find the number   [#permalink] 01 Jul 2019, 08:46