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# If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12

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Joined: 31 Oct 2013
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Concentration: Accounting, Finance
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If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12  [#permalink]

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Updated on: 23 Jan 2018, 20:36
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Difficulty:

15% (low)

Question Stats:

82% (00:53) correct 18% (01:12) wrong based on 77 sessions

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If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12 how many integers will satisfy x?

A. 1
B. 2
C. 3
D. 4
E. none of these

need effective solutions. it is also requested to upload similar questions.

Originally posted by KSBGC on 23 Jan 2018, 16:32.
Last edited by Bunuel on 23 Jan 2018, 20:36, edited 3 times in total.
Renamed the topi and edited the question.
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Joined: 11 Nov 2017
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Re: If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12  [#permalink]

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23 Jan 2018, 16:37
1
5<x<11, 7<x<13 can be combined to gather that x<7<11.
Since x is an integer it can be 8,9 or 10. From x+2<12 we can see that x can be 8 or 9.
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Joined: 02 Aug 2009
Posts: 7952
Re: If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12  [#permalink]

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23 Jan 2018, 18:20
1
selim wrote:
If X is an integer such that 5<x<11, 7<x<13, and x+2<12 how many integers will satisfy x?

a)1
b)2
c)3
d)4
e) none of these

need effective solutions. it is also requested to upload similar questions.

Restrictions on x..
1) it is an integer.
2) 5<x<11
3) 7<x<13
4) x+2<12...x<10..

From above 3 points, 7<x<10, so 8 and 9
TWO values..
B
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Posts: 58315
Re: If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12  [#permalink]

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23 Jan 2018, 20:39
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12  [#permalink]

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26 Jan 2018, 10:45
selim wrote:
If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12 how many integers will satisfy x?

A. 1
B. 2
C. 3
D. 4
E. none of these

We have the following:

For 5 < x < 11, we see that x could be 5, 6, 7, 8, 9, or 10.

For 7 < x < 13, we see that x could be 8, 9, 10, 11, or 12.

Thus, for the first two inequalities, x could be 8, 9, or 10.

We can simplify x + 2 < 12 as x < 10.

Thus, the only integers that satisfy all three inequalities are 8 and 9.

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Re: If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12   [#permalink] 26 Jan 2018, 10:45
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