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# How many integers n are there such that r<n<s?

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Joined: 08 Jun 2017
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How many integers n are there such that r<n<s?  [#permalink]

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27 Sep 2017, 23:49
How many integers n are there such that r<n<s?

1) s-r =5
2) r and s are not integers.

A. Statement (1) Alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) Alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements TOGETHER are sufficient, but neither ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statement (1) and (2) TOGETHER are not sufficient.

This Question is taken from the GMAT Official Guide Review 2017. Kindly post your answers with detailed explanations.

Regards,
Anurup Rao.

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Joined: 26 Jul 2017
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Re: How many integers n are there such that r<n<s?  [#permalink]

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28 Sep 2017, 03:27
Rise Up Scorp! wrote:
How many integers n are there such that r<n<s?

1) s-r =5
2) r and s are not integers.

A. Statement (1) Alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) Alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements TOGETHER are sufficient, but neither ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statement (1) and (2) TOGETHER are not sufficient.

This Question is taken from the GMAT Official Guide Review 2017. Kindly post your answers with detailed explanations.

Regards,
Anurup Rao.

Posted from my mobile device

From statement 1) we get 2 possibilities of types of values of r & s;
case I: r and s are integers: lets say r =2 then s = 7 therefore 2<n<7 and as n is given as an integer then n can take values such as 3,4,5,6 so n can take any of these 4 values.
Case II: r and s are not integers: lets say r = 1.5 and thus s will be 6.5. now 1.5<n<6.5 thus n can be any of 2,3,4,5,6 so n can take any of the 5 values.
Hence this statement 1 is insufficient because it cannot give us a single answer.

From statement 2) r and s are not integers
Clearly insufficient

Combining 1 & 2 we get that case II is valid here, hence n can take 5 values only.
Thus correct option is C
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Re: How many integers n are there such that r<n<s?  [#permalink]

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28 Sep 2017, 11:29
Hi Anurup,

This question can be solved by TESTing VALUES (the approach vishalbalwani used), so I won't rehash any of that work here. In the future, you will likely receive more of a response to your questions if you post them in the appropriate sub-forum. For Example, the DS forum can be found here:

https://gmatclub.com/forum/data-sufficiency-ds-141/

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Re: How many integers n are there such that r<n<s? &nbs [#permalink] 28 Sep 2017, 11:29
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