Official Guide 12th edition Problem no:65

[Touseef]

How many integers are there between, but not
including, integers r and s?

(1) s - r = 10
(2) There are 9 integers between, but not including,
r + 1 and s + 1

The Answer Explanation given in the OG takes all the numbers between 'r' and 's' as Consecutive integers,but is nowhere stated in the Question that these are consecutive integers.

Can anyone explain me the right approach to this problem?

[bblast]

Hi,

I had the same doubt that u have posted when I attempted this question some time back.

However in hindsight its actually a genuine trap.

To prove it just ask yourself.
how many integers are there between 10 and 20 ? We don't need to mention that we are considering consecutive integers, do we ?

[kmittal82]

Hi,

I had the same doubt that u have posted when I attempted this question some time back.

However in hindsight its actually a genuine trap.

To prove it just ask yourself.
how many integers are there between 10 and 20 ? We don't need to mention that we are considering consecutive integers, do we ?

>how many integers are there between 10 and 20
4 even integers
5 odd integers
9 consecutive integers

So, do you think its safe to assume if the question just asks for integers, it include all types of integers? The perils of the GMAT...

[Touseef]

Thanks dude....I get it now

[GmatKiss]

IMO:C what is OA?

[HeintzC2]

The question asks for "How many integers", the term Integer covers even, odd, and consecutive integers.

for (1) s-r = 10; using easy numbers s = 11, r = 1, so s-r=10. There are 9 integers between 1 and 11 (2,3,4,5,6,7,8,9,10). Sufficient.

for (2), there are 9 integers between, but not including r+1 and s+1. Since we know already there are 9 integers between 11 and 1, we can reuse these same numbers.
therefore, r-1 and 0 and s-1 = 10. since we just subtracted 1 from both ends of our group, the number of integers within the group stays the same. there are 9 integers between 0 and 10. Sufficient.

Answer is D

How many integers are there between, but not
including, integers r and s?

(1) s - r = 10
(2) There are 9 integers between, but not including,
r + 1 and s + 1

The Answer Explanation given in the OG takes all the numbers between 'r' and 's' as Consecutive integers,but is nowhere stated in the Question that these are consecutive integers.

Can anyone explain me the right approach to this problem?

[bblast]

@ tauseef- glad it helped

@ mittal- you have to be careful what inference you make from the wording of the question.