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

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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 selim 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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Re: If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12 [#permalink]

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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.
so b) is the answer.
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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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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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Re: If x is an integer such that 5 < x < 11, 7 < x < 13, and x + 2 < 12 [#permalink]

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New post 23 Jan 2018, 20:39
selim wrote:
need effective solutions. it is also requested to upload similar questions.


9. Inequalities



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Hope it helps.
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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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New post 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.

Answer: B
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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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