Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: NEW SET of good PS(3) [#permalink]
28 May 2014, 11:48

Bunuel wrote:

5. Mrs. Smith has been given film vouchers. Each voucher allows the holder to see a film without charge. She decides to distribute them among her four nephews so that each nephew gets at least two vouchers. How many vouchers has Mrs. Smith been given if there are 120 ways that she could distribute the vouchers? (A) 13 (B) 14 (C) 15 (D) 16 (E) more than 16

Answer: C.

Clearly there are more than 8 vouchers as each of four can get at least 2. So, basically 120 ways vouchers can the distributed are the ways to distribute \(x-8\) vouchers, so that each can get from zero to \(x-8\) as at "least 2", or 2*4=8, we already booked. Let \(x-8\) be \(k\).

In how many ways we can distribute \(k\) identical things among 4 persons? Well there is a formula for this but it's better to understand the concept.

Let \(k=5\). And imagine we want to distribute 5 vouchers among 4 persons and each can get from zero to 5, (no restrictions).

Consider:

\(ttttt|||\) We have 5 tickets (t) and 3 separators between them, to indicate who will get the tickets:

\(ttttt|||\) Means that first nephew will get all the tickets,

\(|t|ttt|t\) Means that first got 0, second 1, third 3, and fourth 1

And so on.

How many permutations (arrangements) of these symbols are possible? Total of 8 symbols (5+3=8), out of which 5 \(t\)'s and 3 \(|\)'s are identical, so \(\frac{8!}{5!3!}=56\). Basically it's the number of ways we can pick 3 separators out of 5+3=8: \(8C3\).

So, # of ways to distribute 5 tickets among 4 people is \((5+4-1)C(4-1)=8C3\).

For \(k\) it will be the same: # of ways to distribute \(k\) tickets among 4 persons (so that each can get from zero to \(k\)) would be \((K+4-1)C(4-1)=(k+3)C3=\frac{(k+3)!}{k!3!}=120\).

\((k+1)(k+2)(k+3)=3!*120=720\). --> \(k=7\). Plus the 8 tickets we booked earlier: \(x=k+8=7+8=15\).

Answer: C (15).

P.S. Direct formula:

The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is \(n+r-1C_{r-1}\).

The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is \(n-1C_{r-1}\).

Hope it helps.

-----------------------------

Hi Bunuel, Can you please help solve this problem directly using the formulas provided?

The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is n-1C_{r-1}.

Re: NEW SET of good PS(3) [#permalink]
11 Jul 2014, 22:29

Augustus wrote:

yangsta8 wrote:

Bunuel wrote:

1. ABCDE is a regular pentagon with F at its center. How many different triangles can be formed by joining 3 of the points A,B,C,D,E and F? (A) 10 (B) 15 (C) 20 (D) 25 (E) 30

6 points in total to make triangles. I think a combination of any 3 will make a unique triangle so: 6C3 = 20

Will anyone please explain what the C means in the notation?

Thanks in advance

I guess, 6C3 stands for a Combination formula, i.e. we have 3 choices out of 6 without restrictions. This means 6!/3!*3!=20

Re: NEW SET of good PS(3) [#permalink]
09 Aug 2014, 06:06

Bunuel wrote:

ANSWERS (OAs):

As most of the problems was solved correctly, I'm posting only OAs. Please let me know if anyone needs any clarification.

1. ABCDE is a regular pentagon with F at its center. How many different triangles can be formed by joining 3 of the points A,B,C,D,E and F? (A) 10 (B) 15 (C) 20 (D) 25 (E) 30

Answer: C.

2. The function 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 prime, then f(p) = (A) P-1 (B) P-2 (C) (P+1)/2 (D) (P-1)/2 (E) 2

Answer: A.

3. How many numbers that are not divisible by 6 divide evenly into 264,600? (A) 9 (B) 36 (C) 51 (D) 63 (E) 72

Answer: D.

4.A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale? (A) 20 (B) 36 (C) 48 (D) 60 (E) 84

Answer: C.

5. Mrs. Smith has been given film vouchers. Each voucher allows the holder to see a film without charge. She decides to distribute them among her four nephews so that each nephew gets at least two vouchers. How many vouchers has Mrs. Smith been given if there are 120 ways that she could distribute the vouchers? (A) 13 (B) 14 (C) 15 (D) 16 (E) more than 16

Answer: C.

6. This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year? (A) 1/(r+2) (B) 1/(2r+2) (C) 1/(3r+2) (D) 1/(r+3) (E) 1/(2r+3)

Answer: E.

7. Before being simplified, the instructions for computing income tax in Country Rwere to add 2 percent of one's annual income to the average(arithmetic mean)of 100units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax in Country R's currency, for a person in that country whose annual income is I? (A) 50+I/200 (B) 50+3I/100 (C) 50+I/40 (D) 100+I/50 (E) 100+3I/100

Answer: C.

8. How many positive integers less than 10,000 are such that the product of their digits is 210? (A) 24 (B) 30 (C) 48 (D) 54 (E) 72

Answer: D.

9. Find the number of selections that can be made taking 4 letters from the word"ENTRANCE". (A) 70 (B) 36 (C) 35 (D) 72 (E) 32

Answer:B.

Find in the above word, the number of arrangements using the 4 letters.

Answer:606.

10. How many triangles with positive area can be drawn on the coordinate plane such that the vertices have integer coordinates (x,y) satisfying 1≤x≤3 and 1≤y≤3? (A) 72 (B) 76 (C) 78 (D) 80 (E) 84

Answer: B.

Hello Bunuel, Could you please explain the approaches to solve Q9 and Q10.

Re: NEW SET of good PS(3) [#permalink]
01 Sep 2015, 23:59

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: NEW SET of good PS(3) [#permalink]
05 Oct 2015, 16:33

2. The function 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 prime, then f(p) = (A) P-1 (B) P-2 (C) (P+1)/2 (D) (P-1)/2 (E) 2

Regarding the question 2, I think it should be choice B and not A I agree to the way of solving here . BUT question says f(n) includes all integers LESS than N and does not say including N . Thus if F is a prime, shouldnt it be n-1(as n is not included) and another -1 (as 1 is a common factor, Thus n-2.

Re: NEW SET of good PS(3) [#permalink]
06 Oct 2015, 03:52

Expert's post

shreyashid wrote:

2. The function 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 prime, then f(p) = (A) P-1 (B) P-2 (C) (P+1)/2 (D) (P-1)/2 (E) 2

Regarding the question 2, I think it should be choice B and not A I agree to the way of solving here . BUT question says f(n) includes all integers LESS than N and does not say including N . Thus if F is a prime, shouldnt it be n-1(as n is not included) and another -1 (as 1 is a common factor, Thus n-2.

Apologies if I am wrong. PLease correct me .

That's not correct. There is no reason whatsoever to exclude 1: 1 also does not have have a common factor with say 7 other than 1. So, you should include 1 as well. _________________

On September 6, 2015, I started my MBA journey at London Business School. I took some pictures on my way from the airport to school, and uploaded them on...

When I was growing up, I read a story about a piccolo player. A master orchestra conductor came to town and he decided to practice with the largest orchestra...

Amy Cuddy, Harvard Business School professor, at TED Not all leadership looks the same; there is no prescribed formula for what makes a good leader. Rudi Gassner believed that...

We are thrilled to welcome the Class of 2017 to campus today, and data from the incoming class of students indicates that Kellogg’s community is about to reach a...