GMAT Questions #1

Posted: August 3, 2010 by kdawgz in GMAT

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) =

  1. p-1
  2. p-2
  3. p+1/2
  4. p-1/2
  5. 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 2:4root3

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)

  1. 10 of the integers in S are even
  2. 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:

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH Statement ALONE is sufficient.
  5. 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!

  1. 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

  2. kdawgz says:

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

  3. lol okay the time for my post was messed 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!!

  4. KK, study notes:
    First off, you need to understand PRIME NUMBERs better!! (QA, QC)
    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.

  5. kdawgz says:

    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!

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