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

This topic has 1 expert reply and 0 member replies

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

Post Sun Sep 24, 2017 7:03 am
How many integers n are there such that r < n < s?

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

The OA is C.

I tried to make this DS question. I concluded (E). The number of integers between r and s is constant and independent of r and s? I need a clarification. Please.

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Top Reply
Post Sun Sep 24, 2017 7:12 am
Vincen wrote:
How many integers n are there such that r < n < s?

(1) s - r = 5
(2) r and s are not integers.
Target question: How many integers n are there such that r < n < s?

Statement 1: s - r = 5
There are two cases we need to consider.
Case a: s and r are integers.
For example, s=6 and r=1, in which case there are 4 integers between r and s (2, 3, 4 and 5)
Case b: s and r are not integers.
For example, s=6.1 and r=1.1, in which case there are 5 integers between r and s (2, 3, 4, 5, and 6)

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: r and s are not integers
This is definitely not enough information here to answer the target question.
Consider these 2 cases.
Case a: r=1.1 and s=2.1, in which case there is 1 integer between r and s (2)
Case b: r=1.1 and s=3.1, in which case there are 2 integers between r and s (2 and 3)

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
From statement 1, we know that there are either 4 or 5 integers between r and s, depending on whether or not r and s are integers.
Statement 2 rules out the possibility that r and s are integers.
If r and s are non integers, then there must be 5 integers between r and s

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

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Brent Hanneson – Founder of GMATPrepNow.com
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