I’m one of those ambitious students that is trying to get into a good grad school, namely, the ones below. As GMAT studies continue and exam day is coming up in a couple of weeks, there is still lots of room for improvement.

Here are the few questions that I got wrong and cannot answer myself on the last sample test I did, granted most of the ones I was able to correct myself were silly mistakes anyway:

**A. The function of f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number, then f(p) =**

- p-1
- p-2
- p+1/2
- p-1/2
- 2

Having not done math for awhile, I don’t know where to begin to solve this problem. The correct answer is p-1. An explanation would be appreciated!

**B. If the two regions below have the same area, what is the ratio of t:s?**

I generally understand the rules of geometry and special triangles but an explanation for this answer would be great too. The answer is 2:4r*oot*3

**C. For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75=3x5x5. How many two digit positive integers have length 6?**

This question is confusing because, technically, from what I understand, it is possible for: 1x1x1x1x7x7x2 =98, 1x1x2x2x2x2 = 16, and 1x1x1x1x1x7x7 = 49 etc. But the answer is only TWO. Help.

**D. Set S consists of 20 different positive integers. How many integers in S are odd? (Data sufficiency problem)**

**10 of the integers in S are even****10 of the integers in S are multiples of 4**

So immediately looking at the data given in (1) and (2), statement (1) is definitely sufficient to answer the question. As for statement (2), I thought it was sufficient because all multiples of 4 are multiples of 2 and are therefore even – EXCEPT 1. Maybe that’s where I went wrong. Anyway the answer was: Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question. I originally put each statement alone is sufficient.

Data sufficiency questions have five answer choices:

- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH Statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.

**E. In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?**

The answer is 13 but the method escapes me :(.

I know when I find out what the answer to some of these, I deserve a knock on the head. But no pain no gain. Gotta learn from mistakes!

LOL You actually posted the math questions!! You have the privilege of sharing this blog with a math student =D I’ll take a look…

BTW since you started the post first, it came up before my post. So you probably want to change “one of those listed below” =P

LOL it’s ’cause I fixed the time =P. Thanks for the help =)

lol okay the time for my post was messed up..so I changed it. Now the word “below” makes more sense.

and after I looked at the questions I have to say, you are NOT asian!!

KK, study notes:

First off, you need to understand PRIME NUMBERs better!! (QA, QC)

Second, KNOW THE BASIC GEOMETRIC FORMULAS (QB)

Third, learn to consider EXTREME cases (Max/min, limit) (QC, QE)

Forth, know what exactly is being asked! (any conditions, convert the question/wording, etc) (QC, QD)

I was going to type up the answers but I think I’ll just explain them to you tmrw.

It was quite embarrassing finding out what the answers were to the above questions.

First of all. 1 is NOT a prime number. I wonder what school has taught me all these years. Anyway. The rest were pretty straight forward. Thanks for the help!