How many integers between r and s?

[GmatGreen]

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

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

[Brent@GMATPrepNow]

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

[Patrick_GMATFix]

IN evaluating statement (1), be careful not to assume that r and s are integers. You'll get different answers for (s,r)=(5,0) and (s,r)=(5.5, 0.5). There are 4 integers between 0 and 5, but 5 integers between 0.5 and 5.5 so we cannot definitively answer the question from (1) alone. We have to merge the statements.

The answer is C. I go through the question in detail in the full solution below (taken from the GMATFix App).



-Patrick

[Bill@VeritasPrep]

IN evaluating statement (1), be careful not to assume that r and s are integers. You'll get different answers for (s,r)=(5,0) and (s,r)=(5.5, 0.5). There are 4 integers between 0 and 5, but 5 integers between 0.5 and 5.5 so we cannot definitively answer the question from (1) alone. We have to merge the statements.

The answer is C. I go through the question in detail in the full solution below (taken from the GMATFix App).



-Patrick

Yep, it's a perfect example of how sometimes a statement will provide us a clue about the other one. It's very easy to plug in for R and S and assume that S1 works on its own, but when S2 is something that doesn't seem to help, we have to stop and consider why they would bother providing it. Why is it important that S and R are not integers? From there, it's easier to find the bad assumption in S1.

[[email protected]]

Hi GmatGreen,

As everyone else has already mentioned, thinking about how the answer changes when dealing with integers vs. non-integers is necessary on this question.

Going forward with DS questions, here are some things to note:

1) You won't have to consider decimals and fractions all that often (that level of depth is only required on a handful of DS questions)
2) Look for any "clues" (such as how Fact 2 was written) and "limitations" (the phrase X > 0 means that X cannot be 0 or negative, so what's left? - positive integers and positive fractions) appear in the question to guide you.

GMAT assassins aren't born, they're made,
Rich