BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

ds

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 789
Joined: Sun May 06, 2007 1:25 am
Location: Southern California, USA
Thanked: 15 times
Followed by:6 members

ds

by resilient » Tue Apr 22, 2008 8:54 pm
Is the integer n a multiple of 21?

1. n is a multiple of 14.
2. n - 12 is a multiple of 3.

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



qa is C but I chose E.

AFter drawing out the possibilites I got sometimes for C.. ANy help?
Appetite for 700 and I scraped my plate!
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3380
Joined: Mon Mar 03, 2008 1:20 am
Thanked: 2256 times
Followed by:1535 members
GMAT Score:800

by lunarpower » Thu Apr 24, 2008 1:43 am
let's assume that you have eliminated A, B, D, because both statements individually are insufficient. (if you need help reaching that conclusion as well, please post and say so, but the fact that you are considering C vs E indicates that you've already gotten that far.)

--

let's take the two statements together. perhaps the easiest way to do this is to look for patterns in the data.

the numbers satisfying statement (1) are
14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ...

of these, the ones satisfying statement (2) are boldface:
14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ...

you can see the pattern: every third number is boldface, and these are exactly the numbers that are multiples of 42 (and therefore also multiples of 21).

sufficient
answer = c

--

here's the theory-based solution.

statement (1) says that n is equal to 14x, for some whole number x.
statement (2) says that n - 12 is divisible by 3.

taking the two statements together, we have that
14n - 12 is divisible by 3
which means that 14n itself is divisible by 3 (because 12 is divisible by 3)
which means that n is divisible by 3, because there are no 3's in the prime factorization of 14.

sufficient
answer = c
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron
Top
Post new topic Post Reply
• Page 1 of 1