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# How many integers k are there such that 1<7k-14<49

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Senior CR Moderator
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How many integers k are there such that 1<7k-14<49 [#permalink]

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10 Apr 2017, 20:34
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Difficulty:

25% (medium)

Question Stats:

67% (00:44) correct 33% (00:47) wrong based on 72 sessions

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How many integers k are there such that $$1<7k-14<49$$ ?

A. 7
B. 6
C. 5
D. 4
E. 3

Source: GMAT Free

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Math Expert
Joined: 02 Sep 2009
Posts: 46129
Re: How many integers k are there such that 1<7k-14<49 [#permalink]

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10 Apr 2017, 22:10
nguyendinhtuong wrote:
How many integers k are there such that $$1<7k-14<49$$ ?

A. 7
B. 6
C. 5
D. 4
E. 3

Source: GMAT Free

$$1<7k-14<49$$

Add 14 to all parts: $$15<7k<63$$

Divide by 7: $$2\frac{1}{7}<k<9$$

k can be 3, 4, 5, 6, 7, and 8.

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Joined: 14 Jun 2016
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Re: How many integers k are there such that 1<7k-14<49 [#permalink]

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10 Apr 2017, 22:22
Ans: A
Becoz write down numbers from 2 to 9 and multiply it by 7. This numbers will be below 49.
If you take above 9 this numbers will be greater than 49.
If you take the negative integers you will get negative numbers in the intervals which is not true.

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Math Expert
Joined: 02 Sep 2009
Posts: 46129
How many integers k are there such that 1<7k-14<49 [#permalink]

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10 Apr 2017, 22:31
subhash29 wrote:
Ans: A
Becoz write down numbers from 2 to 9 and multiply it by 7. This numbers will be below 49.
If you take above 9 this numbers will be greater than 49.
If you take the negative integers you will get negative numbers in the intervals which is not true.

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Neither 2 nor 9 satisfies the given inequality. The correct answer is B, not A. For OA you can check OA spoiler in the original post. You can also check the post above yours for correct solution.
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Joined: 14 Jun 2016
Posts: 4
Re: How many integers k are there such that 1<7k-14<49 [#permalink]

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10 Apr 2017, 22:42
Yeah, that's correct.
Thnx a lot bunuel

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Re: How many integers k are there such that 1<7k-14<49 [#permalink]

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18 Apr 2017, 16:33
nguyendinhtuong wrote:
How many integers k are there such that $$1<7k-14<49$$ ?

A. 7
B. 6
C. 5
D. 4
E. 3

We can simplify the given inequality.

1 < 7k - 14 < 49

15 < 7k < 63

15/7 < k < 63/7

2 1/7 < k < 9

Thus, k can be 3, 4, 5, 6, 7, or 8.

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Re: How many integers k are there such that 1<7k-14<49   [#permalink] 18 Apr 2017, 16:33
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