If n is a positive integer

[v123]

Data Sufficiency: If n is a positive integer and r is a remainder when (n-1)(n+1) is divided by 24, what is the value of r?
(1) n is not divisible by 2
(2) n is not divisible by 3

Not sure where to start

[mondegreen]

Data Sufficiency: If n is a positive integer and r is a remainder when (n-1)(n+1) is divided by 24, what is the value of r?
(1) n is not divisible by 2
(2) n is not divisible by 3

Not sure where to start

First statement, assume n=1-->(n-1)(n+1) = 0, and remainder(r) = 0 when divided by 24.
Similarly, assume n=3-->(n-1)(n+1) = 8, and remainder(r) = 8, when divided by 24. NO unique numerical value, Insufficient.

Second statement,assume n=1, just as above, and r=0.Again, assume n=2, and r = 3. Insufficient.

Now,taking both statements together, you can plugin 2-3 values, like n=5,7,25 etc and you will realise that it is always divisible by 24.

C.

Else, another method to prove it algebraiclly:

Taking both statements together, we know that n is odd. Thus, (n-1) and (n+1) are even.Again, (n-1) and (n+1) are consecutive even integers, and product of any 2 consecutive integrs is ALWAYS divisible by 8.

Any product of 3 consecutive integers : (n-1)*(n)*(n+1) is ALWAYS divisible by 3. Thus, as n is not divisible by 3, (n-1)(n+1) has to be divisible by 3.

Thus, (n-1)*(n+1) is always divisible by 3 and 8 --> Divisible by 24 too.

C.

[RonPurewal]

Hi,
You've been offered one solution by the poster above. To receive a response from MGMAT staff, though, please write something about what you've already tried / what you already understand about the problem.
The GMAT PREP software now has answer keys. So, if you don't write any specific questions, the best response is that you should check out the existing answer key. (If we typed up a complete response here, it would very likely be almost identical to the answer key that's already there.)

So please go ahead and check out the answer key that came with the question. If there's still something you don't understand, then tell us what you tried, and what you did understand, and we'll take it from there.

Thanks.

[v123]

Thanks Ron, my question was whether there was another strategy other than trying numbers. If not, is there a guideline on how to best try out numbers to reach a conclusive answer?

[RonPurewal]

Thanks Ron, my question was whether there was another strategy other than trying numbers.

Well, if you know certain facts about these things, you can use those instead.

* Every other integer is a multiple of 2.
So, if n is NOT a multiple of 2, then both (n - 1) and (n + 1), the two neighboring integers, are multiples of 2.

* Every third integer is a multiple of 3.
So, exactly one of (n - 1), n, (n + 1) has to be a multiple of 3. If it's not n, it must be one of the other two.

In either case, you know the remainder is going to be 0.

[RonPurewal]

If not, is there a guideline on how to best try out numbers to reach a conclusive answer?

If the numbers are in a strict order with an easy pattern, then you should just go ahead and test them in exactly that order.

So, for statement 1, you should try 1, 3, 5, etc., until you see a pattern (which shouldn't take long).
For statement 2, you should try 1, 2, 4, 5, etc., until you see a pattern (which, again, shouldn't take long).

[angierch]

Hi Ron,

When you say that the GMAT prep has the key answers, do you refer to the GMAT explaining the correct answer? If this is true, where can I find these explanations? I downloaded the last version of the GMAT prep and can't find the explanations for the correct answers.

[RonPurewal]

I thought that the "new" GMAT Prep (released sometime in mid 2012, if I remember correctly -- could have been mid 2013, though) had answer keys to all the questions.

Maybe it's just the paid question packs. Those definitely have answer keys. But I thought there were now keys for all the questions in the free software, too.

I could definitely be wrong about this.

[sunilpk8]

First statement, assume n=1-->(n-1)(n+1) = 0, and remainder(r) = 0 when divided by 24.
Similarly, assume n=3-->(n-1)(n+1) = 8, and remainder(r) = 8, when divided by 24. NO unique numerical value, Insufficient.

Second statement,assume n=1, just as above, and r=0.Again, assume n=2, and r = 3. Insufficient.

Now,taking both statements together, you can plugin 2-3 values, like n=5,7,25 etc and you will realise that it is always divisible by 24.

C.

when taking 1 & 2 why did we not check for n=1 . please advise

[RonPurewal]

if you use n = 1, you get the same answer (remainder = 0) as you get from all the other cases listed. so, nothing changes. same answer either way.

[RonPurewal]

more generally, this is how the test will always work. the problems won't depend on cases that are "weird".
yes, "weird" is a somewhat subjective term. but, here's what i mean: if you didn't learn about a certain case when you first learned a particular concept, then you won't need to worry about that case on the test.

here:
when you first learned remainders, there's no way you discussed the remainder when 0 is divided by some other number. (more generally, you didn't discuss the remainder of m/n if m is less than n.)
so, these cases--if they apply--WILL NOT affect the outcome of the problem.