Inconsistency? Divisibility - CAT 3 - Question #3

[michaeltrex]

Okay, unless I'm reading this wrong, there is an inconsistency between these two questions?
On CAT #3, question #3 states:

"Is n/18 an integer?"
(1) 5n/18 is an integer
(2) 3n/18 is an integer

In the Number Properties Guide book on page 77, a very similar question states:

"If p is an integer, is p/18 an integer?"
(1) 5p/18 is an integer
(2) 6p/18 is an integer

As you can see, both questions and answers are very similar. CAT #3 says statement 1 is insufficient. However, in the guide book, it says statement 1 is sufficient. Let's take a step back and rephrase the question. "Are there two 3's and a 2 in p's prime box?" Looking at statement one, this should be sufficient, because there are (at least) two 3's and a 2 in p's prime box. Why does this guide book say statement one is sufficient, but exam #3 says it's insufficient??????

[Captain]

There is an important difference between the 2 questions. In your referred guide the question explicitly stated that 'p' is an integer. In the test qustion 'n' may need not be an integer. For the CAT question refer to the link below for explanation.

http://www.manhattangmat.com/forums/is-n-18-an-integer-1-5n-18-is-an-integer-2-3n-18-is-t636.html

[michaeltrex]

Thank you

[StaceyKoprince]

Thanks, Captain! Doing my work for me! :)

[vineetagrwal]

Is the correct answer E?

[RonPurewal]

Is the correct answer E?

to which problem?

the first problem is C. here's why:

statement 1 alone:
if 5n/18 = 5, then n = 18, for which n/18 is an integer; if 5n/18 = 1, then n = 18/5, which is not an integer (and so therefore n/18 isn't an integer either). insufficient.
note that we are picking values for 5n/18, NOT values for n - per the problem statement!

statement 2 alone: reduce 3n/18 to n/6 to make this statement easier to think about.
if n/6 = 3, then n = 18, for which n/18 is an integer; if n/6 = 1, then n = 6, for which n/18 is not an integer. insufficient.
note that we are picking values for 3n/18, NOT values for n - per the problem statement!)

together:
remember that sums and differences of integers are also integers.
if 5n/18 and 3n/18 are integers, then 5n/18 - 3n/18 = 2n/18 is also an integer. once we have that, 3n/18 - 2n/18 = n/18 is also an integer. sufficient.

--

the second problem is A, mostly because 6 is a factor of 18 but 5 isn't. i can provide further explanation if necessary; please post back.