GMAT Math

This post is for:
1.) People who want to do well in DS questions and are struggling.
2.) People who are striving for a Q50/51 and have fairly good understanding of DS questions and basic quant concepts.

This post is not for:
People who have JUST started their preparation and are not very comfortable with DS questions. They might benefit from this post, but personally I feel they should bookmark it to read it at a slightly later stage in their preparation.

The Data Sufficiency Banana:

Imagine you are going on a 500 mile road trip. You know you cannot survive without eating a banana every 50 miles. You have 11 bananas at home. How many bananas will you want to carry then? Just 10? Or all 11? Would you not want to keep that extra one for safety? - Just to reassure yourselves that if you lose 1, you have 1 more at your disposal ?

Similarly, on a DS question, would you not want to have that 1 extra bit of information to keep you safe? Wouldn't that help you? Now, the question is how GMAT gives you that extra banana.

The toughest questions on GMAT quant are DS questions that look easy. Note this somewhere. If you are aiming for Q 49/50/51, don't take anything for granted. Anything !
Back to the banana. So where is that extra information in the DS question? It is not in statement 1 and it is not in statement 2 either. You will get it when you combine the two.
Ever noticed how every time the information across the two statements is consistent? You can always use THIS information if you are struggling on a DS question.

Try to solve this*:
The integers m and p are such that 2 is less than m and m is less than p. Also, m is not a factor of p. If r is the remainder when p is divided by m, is r > 1.
(1) The greatest common factor of m and p is 2.
(2) The least common multiple of m and p is 30.

Hmm.. interesting. So let us start by plugging numbers.
Given: 2<m<p and m,p are integers. Also p is not = km (assume k to be any positive integer constant).

Statement 1:
So GCF of m and p is 2. Okay let me put some numbers then.
4 and 6: remainder 2. 6 and 8 remainder 2. 4 and 10 remainder 2. 8 and 14 remainder 6. 8 and 18 remainder 2.
Its pretty obvious from the pattern that you would not get anything less than 2 because you are dealing with only even numbers here. So remainder is definitely greater than 1. ---- SUFFICIENT

Statement 2:
LCM of m and p is 30.
Hmm.. I can think of 3 and 10. 5 and 6. 2 and 15. I seem to be stuck with only these pairs. So let me proceed further.
I eliminate 2 and 15 because it is given that m>2.
5 and 6 - remainder 1. 3 and 10 - remainder 1. So every remainder is coming out to be 1 in the end. I go ahead and say we know for sure that remainder is not greater than 1 - SUFFICIENT

The official answer to this problem is A.

Let us re-analyse what we missed in statement 2.
There has to be some other pair of numbers that has remainder greater than 1 and has an LCM of 30.

Let us see how I could have avoided this mistake. Because I know statement 1 and statement 2 have to be consistent let me use this knowledge.

Of all the numbers I wrote, did any of the pair satisfy Statement 1? Did any of the pairs have a gcf of 2?
Do 3 and 10 have a gcf of 2? No. Do 5 & 6 have a gcf of 2? No.
So what pair have I missed?

what should I look for? gcf = 2 and lcm = 30. After scribbling a bit and through some random guessing I come up with 6 and 10. That is the pair I was looking for.

Alternatively (for a sure shot proof):

Let me use this formula to get to that pair: GCF (n1,n2) X LCM (n1,n2) = n1 X n2
That means here: 2 X 30 = n1 X n2 = 60 = 6 X 10 This implies N1= 6, N2= 10 (of all the other factors, only 6 and 10 satisfy the condition that n1>2 and gcf =2 )

Through using this EXTRA information that both the statements are consistent you should check your answer whenever possible. I'm not asking you to use this everywhere. You might end up losing a lot of time in that case. Only in two cases: if you are stuck or if you want to validate your solution.

NOTE: This information is extra and you would not require it to solve the questions. Use it as a last resort when you are stuck or to check your answer. More importantly KNOW that you have this weapon in your arsenal while solving DS questions.


Cheers!

*I'm not an expert and not affiliated to any of the test prep companies. This question might be from GMAC/MGMAT/Kaplan/Princeton/"any other place not on this list".
**I will entertain no questions on where that "banana" thing came from

Nice post... Definitely true that when the answer is D, your solution will be the same for each statement.