Bunuel 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 The students who (incorrectly) conclude that statement 1 is sufficient make the very common mistake of assuming r and s are integers, even though the question doesn't state this. Since the question doesn't specifically state whether r and s are integers, there are many different pairs of values but that satisfy the condition that s - r = 5. Here are two:
Case a: r = 2 and s = 7. Here, n can equal 3, 4, 5 or 6, which means the answer to the target question is
there are 4 integer values of n such that r < n < sCase b: r = 2.1 and s = 7.1. Here, n can equal 3, 4, 5, 6 or 7, which means the answer to the target question is
there are 5 integer values of n such that r < n < sSince we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Note: We can generalize the above results as follows:
- If r and s are integers, then there are 4 possible integer values of n such that r < n < s
- If r and s are not integers, then there are 5 possible integer values of n such that r < n < s Statement 2: r and s are not integers.Since we aren't told how far apart the values of r and s are, statement 2 is NOT SUFFICIENT
If you're not convinced, here are two conflicting pairs of values for r and s that satisfy statement 2:
Case a: r = 2.1 and s = 4.1. Here, n can equal 3 or 4, which means the answer to the target question is
there are 2 integer values of n such that r < n < sCase b: r = 2.1 and s = 3.4. Here, n can equal 3 only, which means the answer to the target question is
there is 1 integer value of n such that r < n < sSince we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Now that we know
s - r = 5 AND
r and s are not integers, we can apply our
generalization above, which means the answer to the target question is
there are 5 integer values of n such that r < n < sSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
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