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# On Tuesday, Kramer purchases exactly 3 new shirts, 2 new

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Manager
Joined: 01 Nov 2007
Posts: 125
On Tuesday, Kramer purchases exactly 3 new shirts, 2 new  [#permalink]

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18 Jan 2008, 08:35
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100% (00:19) correct 0% (00:00) wrong based on 29 sessions

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On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
A.Tuesday
B. Wednesday
C.Thursday
D. Friday
E. Saturday

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Director
Joined: 12 Jul 2007
Posts: 833

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18 Jan 2008, 08:55
Quote:
1. To get the number of possible outfits we multiply the number of each new article of clothing together.

$formdata=3*2*4+=+24$

Think of it this way. He has 3 ways to wear shirts S1, S2, S3 and 2 ways to wear his new sweaters W1, W2. Together this makes for 6 combinations:

S1-W1
S1-W2
S2-W1
S2-W2
S3-W1
S3-W2

He has 6 ways to wear the shirt and sweatshirt, then just multiply by 4 because he has 4 different hats he can wear was well.

Now we know he has 24 outfits to wear. Let's go about finding the day of the week:

He starts wearing the outfits on Wednesday. That means that in 7 days it will be Wednesday again and he will have gone through 7 outfits. In 21 days it will be Wednesday again and he will have gone through 21 outfits. This means Thursday he will have gone through 22. Friday 23. Saturday 24. He can't wear anything new on a Saturday.

SVP
Joined: 29 Mar 2007
Posts: 2379

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18 Jan 2008, 15:57
JCLEONES wrote:
On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
A.Tuesday
B. Wednesday
C.Thursday
D. Friday
E. Saturday

Simple combinatorics. 2*3*4 = 24 days possible combinations.

Starts Wednesday. F=24 days. But we must count the next day so its

Saturday

E.
SVP
Joined: 04 May 2006
Posts: 1611
Schools: CBS, Kellogg

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18 Jan 2008, 19:40
GMATBLACKBELT wrote:
JCLEONES wrote:
On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
A.Tuesday
B. Wednesday
C.Thursday
D. Friday
E. Saturday

Simple combinatorics. 2*3*4 = 24 days possible combinations.

Starts Wednesday. F=24 days. But we must count the next day so its

Saturday

E.

Agree E,
But first I choose D, I missed the point of question asked. When I see it again, the point is "On which day is this no longer possible? "

Thanks guy!
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Intern
Joined: 19 Jan 2008
Posts: 1

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19 Jan 2008, 15:53
Min number of days after Tuesday = 3*2*4 = 24

Last Day = Tuesday + mod(24,7) = Friday

So, the first day the condition fails falls on a Saturday.
Director
Joined: 03 Sep 2006
Posts: 771

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19 Jan 2008, 23:46
JCLEONES wrote:
On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
A.Tuesday
B. Wednesday
C.Thursday
D. Friday
E. Saturday

Total number of combinations possible

$$3C1*2C1*4C1 = 24$$

For 24 days he can wear different combinations

( 1st day ) Wednesday + 7days ( another Wednesday) + 7days ( another Wednesday) +7days ( another Wednesday)+ Thursday +Friday

So from Saturday he finishes all his combinations and needs to go to market again
Non-Human User
Joined: 09 Sep 2013
Posts: 10947
Re: On Tuesday, Kramer purchases exactly 3 new shirts, 2 new  [#permalink]

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20 Jul 2017, 04:48
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This discussion does not meet community quality standards. It has been retired.

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To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: On Tuesday, Kramer purchases exactly 3 new shirts, 2 new   [#permalink] 20 Jul 2017, 04:48
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