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Multiples - GMAT Prep

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rosh26: Master | Next Rank: 500 Posts; Posts: 215; Joined: Mon Apr 21, 2008 8:07 am

by rosh26 » Tue Jun 17, 2008 3:39 am

Is integer n a multiple of 15?

I n is a multiple of 20

II n+6 is a multiple of 3

Answer is C

Can someone please explain?

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Source: Beat The GMAT — Data Sufficiency | Tue Jun 17, 2008 3:39 am

codesnooker: Legendary Member; Posts: 543; Joined: Fri Jan 18, 2008 1:01 am; Thanked: 43 times; GMAT Score:580

by codesnooker » Tue Jun 17, 2008 5:15 am

It is a very simple question.

According to statement (1), n is a multiple of 20.

i.e n = 20x, where x = ....-3, -2, -1, 0, 1, 2, 3......

So n = .....-60, -40, -20, 0, 20, 40, 60,.....

But still n can be and can not be multiple of 15. Hence, Statement (1) is alone insufficient. Therefore, (A) and (D) are out.

According to statement (2), n+6 is multiple of 3.

i.e. (n+6) = 3x, where x = ....-3, -2, -1, 0, 1, 2, 3......
So n = .....--3, 0, 3, 6, 9, 12, 15, 18, 21,..30, 60, 90

But still n can be and can not be multiple of 15. Hence, Statement (2) is alone insufficient. Therefore, (B) is also out

Now lets take both the statements together,

So, -40, -20, 20, 40 etc are out. and only with n = ....-120, -60, 0, 60, 120....

Which is multiple of 15. Hence, both statements together are sufficient.

HTH...

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ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Thu Jun 19, 2008 12:09 pm

Can there be any underlying rule that if n is a multiple of 3 (from statement b, we know that n is a multiple of 3) and if n is a multiple of 20, for both statements to be true, n MUST be a multiple of 15? I was just hoping if we can solve this problem with out picking numbers by looking at some underlying rule ? Any suggestions?

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: Multiples - GMAT Prep

by Ian Stewart » Thu Jun 19, 2008 12:38 pm

rosh26 wrote:Is integer n a multiple of 15?

I n is a multiple of 20

II n+6 is a multiple of 3

Answer is C

Can someone please explain?

Yes, there's no need to pick numbers here. The question asks 'Is n a multiple of 15'. It's a divisibility question, so it will normally be best to think about prime factorizations. We can translate the question:

Is n a multiple of 15 --> Is n a multiple of 3*5 --> Is n a multiple of both 3 and 5?

From 1: n is a multiple of 20 --> n is a multiple of 2^2*5. We don't care about the 2s for this question, but this does tell us that n is a multiple of 5. Not sufficient- we need to know if n is a multiple of 3 as well.

From 2: n+ 6 is a multiple of 3. Notice this just means that n is a multiple of 3 (if you add or subtract 6 from a multiple of 3, you'll get another multiple of 3). Not sufficient- we need to know if n is a multiple of 5.

From 1+2: we know n is a multiple of 3 and 5, which is what we wanted.

As a general note (and as a partial response to ildude's question in another thread, about working on DS questions), it is often very helpful on DS questions to translate the information given into more useful information. DS questions often do not present information in the most intuitive way. Here, for example, we had to translate the information into information about primes. In other questions, you might see equations like |x| = -x. That may look a bit confusing at first glance, but when you notice it just means that x is negative, it's a lot easier to think about.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Thu Jun 19, 2008 8:00 pm

As always, nice to see your great explanation. Thanks a bunch.

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getbig: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Mar 14, 2007 5:35 pm

by getbig » Wed Feb 11, 2009 12:41 am

Many thanks Ian.. your explanation was fantastic.

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glorydefined: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Tue Mar 31, 2009 9:54 am; Thanked: 2 times

by glorydefined » Thu Sep 10, 2009 12:57 pm

hi Ian,

that piece of information ( |x|=-x ; is nothing but x is -ve)is awesome....ive been looking for stuff like this, could you please post more such things related to inequalities and modulus equations???

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inmate: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Tue Jun 08, 2010 12:09 am

by inmate » Wed Oct 06, 2010 1:18 pm

What does it mean when we say multiple of a #?

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