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apoorva.srivastva: Master | Next Rank: 500 Posts; Posts: 146; Joined: Wed Aug 27, 2008 5:41 am; Thanked: 3 times

SETS AGAIN!!!! :(

by apoorva.srivastva » Mon Jan 18, 2010 6:01 am

Set X, Y, and Z consists positive multiples of 4, 5, and 6, respectively. If Set A is the
intersection of X and Y, set B is the intersection of Y and Z, what is the least possible number
of intersection of A and B?
A. 30
B. 60
C. 90
D. 120
E. 240

B

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Source: Beat The GMAT — Problem Solving | Mon Jan 18, 2010 6:01 am

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

by sanju09 » Mon Jan 18, 2010 6:38 am

apoorva.srivastva wrote:Set X, Y, and Z consists positive multiples of 4, 5, and 6, respectively. If Set A is the
intersection of X and Y, set B is the intersection of Y and Z, what is the least possible number
of intersection of A and B?
A. 30
B. 60
C. 90
D. 120
E. 240

B

Obviously 60.

A the least X int Y is 20 and B the least Y int Z is 30; therefore the least possible number of intersection of A and B is the LCM of 20 and 30 that is 60.

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Quantitative Instructor
The Princeton Review - Manya Abroad
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sreak1089: Master | Next Rank: 500 Posts; Posts: 379; Joined: Wed Jun 03, 2009 3:05 am; Thanked: 19 times; Followed by:1 members; GMAT Score:690

by sreak1089 » Mon Jan 18, 2010 8:48 am

Set A = Intersection of X & Y => Set A contains multipes of 20
Set B = Intersection of Y & Z => Set B contains multiples of 30

Least possible number of Intersection of Set A & B is nothing but LCM of 20 & 30, which is 60.
Hence ans is B.

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diegow77: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sat Dec 05, 2009 8:39 pm; Thanked: 1 times

by diegow77 » Mon Jan 18, 2010 10:31 pm

what is LCM? I got the 20 and 30 but I'm clueless on the whole picture of this problem.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Tue Jan 19, 2010 1:39 pm

diegow77 wrote:what is LCM? I got the 20 and 30 but I'm clueless on the whole picture of this problem.

This question is a very convoluted means of asking:

"What's the lowest common multiple of 4, 5 and 6?"

("LCM" = "Lowest Common Multiple".)

Set A is all the common multiples of 4 and 5; set B is all the common multiples of 5 and 6. So, the smallest member common to both sets A and B will be the lowest common multiple of 4, 5 and 6, which is 60.

To find the lowest common multiple, we can either use brute force or prime factors.

Brute force is pretty quick when dealing with small numbers. We just write all the multiple of the biggest number until we find a number that's divisible by all the numbers on our list:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60... done!

Of course, we can use common sense/logic to speed up the process; we know we need a "5" in our number, so we can just jump to multiples of both 5 and 6:

30 (4 doesn't go in)
60 (4 does go in - done!)

We can also use primes:

4 = 2*2
5 = 5
6 = 2*3

So, our LCM must contain two "2"s, one "3" and one "5" to accomodate all our numbers:

2*2*3*5 = 60