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 500,000 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:

Two integers will be randomly selected from sets A and B [#permalink]

Show Tags

24 Oct 2012, 22:05

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

58% (02:18) correct
42% (00:58) wrong based on 181 sessions

HideShow timer Statistics

A = {2, 3, 5, 7, 11} B = {2, 4, 6, 13}

Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?

Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?

a)15 b)16 c)19 d)20 e)36

It can be easily done by making pairs, but can somebody tell me how to do it using combinations or some other short-cut ?
_________________

Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?

a)15 b)16 c)19 d)20 e)36

This would be the generic strategy:

Step 1: Find out the number of products you get. 5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20

Step 2: Remove the products that appear more than once. Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.

2, 3 2, 4, 6 The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.

Answer = 20 - 1 = 19

Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.
_________________

Re: Two integers will be randomly selected from sets A and B [#permalink]

Show Tags

31 Jan 2013, 11:16

Karishma,

I don't understand this part of your explanation: "Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B."

I don't understand this part of your explanation: "Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B."

Why do we have to do that? Thanks!

This is part of your step 2: Remove the products that appear more than once. The logic here is that a product involving 5/7/11/13 will not appear more than once. So we ignore these numbers.

Say we select 5 from A. Now, when we select any number from set B, we get a distinct product i.e. we get 4 distinct products (5*2, 5*4, 5*6, 5*13) Now think, can you select a number other than 5 from set A and some number from set B to make one of these 4 products? i.e. Without selecting 5 from set A, can you make a product of 10 or 20 or 30 or 65? No, because to make 10/20/30/65, you need a 5 but you have no other 5 or multiple of 5. Same is the case with 7, 11 and 13 (primes that appear only once in one set). So the products made by these prime numbers will not appear more than once.

You don't really need to think all this during your test. Lots of practice and thorough analysis will make these things intuitive.
_________________

Re: Two integers will be randomly selected from sets A and B [#permalink]

Show Tags

31 Jan 2013, 23:43

1

This post received KUDOS

By looking at Set A, we can see that it's all primes. Thus, we should immediately break down the elements in Set B to their prime factors. That gives :

Set A = {2,3,5,7,11}

Set B = {2, 2x2, 3x2, 13}

Apart from 2x3x2 (taking 2 from set A) which is the same as 3x2x2(taking 3 from set A); there is nothing which can be repeated. Thus, the total unique product = 20-1 = 19.
_________________

Re: Two integers will be randomly selected from sets A and B [#permalink]

Show Tags

08 Aug 2014, 13:45

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: Two integers will be randomly selected from sets A and B [#permalink]

Show Tags

06 May 2016, 00:29

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.
_________________

Best Schools for Young MBA Applicants Deciding when to start applying to business school can be a challenge. Salary increases dramatically after an MBA, but schools tend to prefer...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...