wear for the party

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

by sanju09 » Sat Jul 28, 2012 1:57 am

Adam has a certain number of jeans and a certain number of T-shirts to wear for a party. Is the possible number of ways in which Adam can wear a jeans and a T-shirt for the party, a multiple of 6?
I. Adam has a total of 25 jeans and T-shirts to wear for the party.
II. Adam has 50 percent more T-shirts than jeans to wear for the party.

Made up

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Source: Beat The GMAT — Data Sufficiency | Sat Jul 28, 2012 1:57 am

eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

by eagleeye » Sat Jul 28, 2012 2:37 am

sanju09 wrote:Adam has a certain number of jeans and a certain number of T-shirts to wear for a party. Is the possible number of ways in which Adam can wear a jeans and a T-shirt for the party, a multiple of 6?
I. Adam has a total of 25 jeans and T-shirts to wear for the party.
II. Adam has 50 percent more T-shirts than jeans to wear for the party.

Made up

I. Adam has a total of 25 jeans and T-shirts to wear for the party.
Case 1: jeans = 24, Ts =1. 24 is a multiple of 6.
Case 2: jeans = 23, Ts=2. 46 is not a multiple of 6.
Insufficient.

II. Adam has 50 percent more T-shirts than jeans to wear for the party.
T = 1.5J
Since number of Ts must be a positive integer, T(min)= 3, J(min) = 2.
In this case, no. of ways = 3*2 = 6 is a multiple of 6.
Clearly if there were more Ts and Jeans in 3:2 ratio, No. of combinations will continue to be be a multiple of 6.
Sufficient.

B is correct.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Mar 18, 2013 4:49 am

sanju09 wrote:Adam has a certain number of jeans and a certain number of T-shirts to wear for a party. Is the possible number of ways in which Adam can wear a jeans and a T-shirt for the party, a multiple of 6?
I. Adam has a total of 25 jeans and T-shirts to wear for the party.
II. Adam has 50 percent more T-shirts than jeans to wear for the party.

Target question: Is the possible number of ways in which Adam can wear a jeans and a T-shirt for the party, a multiple of 6?

Let T = # of T-shirts Adam owns
Let J = # of jeans Adam owns
So, the total number of outfits = JT

Rephrased target question: Is JT a multiple of 6?

Statement 1: Adam has a total of 25 jeans and T-shirts
There are several pairs of values that meet this condition. Here are two:
Case a: J=1 and T=24, in which case JT is a multiple of 6
Case b: J=2 and T=23, in which case JT is not a multiple of 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Adam has 50 percent more T-shirts than jeans to wear for the party.
In other words, T = 1.5J = (3/2)J
Multiply both sides by 2 to get 2T = 3J
This tells us that T must be a multiple of 3, and J must be a multiple of 2.
From this, we can conclude that JT is a multiple of 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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