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On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and

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On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and  [#permalink]

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New post 30 Oct 2014, 09:27
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D
E

Difficulty:

  75% (hard)

Question Stats:

58% (02:01) correct 42% (01:54) wrong based on 160 sessions

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Tough and Tricky questions: Combinations.



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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Re: On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and  [#permalink]

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New post 30 Oct 2014, 17:10
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Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3
Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 = 2
Hat combinations = 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4

Total Combinations = Shirt Combos*Sweater Combos*Hat Combos
3*2*4=24 combinations

24 / 7 (days of the week) = remainder of 3

Purchased on Tuesday, 3rd day is Friday. Next day, which he won't have a new combination for, is Saturday. (E)
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Re: On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and  [#permalink]

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New post 30 Oct 2014, 17:32
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Bunuel wrote:

Tough and Tricky questions: Combinations.



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 combinations of Shirts, Sweaters and Hats - 3*2*4 = 24
So, on 25th day, he'll have to repeat a combination. So, starting Wed, 25th day is Sat.

Ans. E
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Re: On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and  [#permalink]

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New post 03 Jan 2015, 21:25
From wednesday till saturday he can use 4 different hats after that he will run out of options...Hence Saturday E.
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On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and  [#permalink]

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New post 04 Jan 2015, 06:38
Total combinations possible =3*2*4=24
So 24 days different combinations are possible
( 7 days in a week )

21 st day- tuesday
22 nd day- wednesday
23 rd day- thursday
24 th day- friday

On 25 th day i.e. saturday different combination is not possible
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Re: On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and  [#permalink]

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New post 10 Apr 2019, 22:48
Bunuel wrote:

Tough and Tricky questions: Combinations.



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


3 Shirts * 2 Sweaters * 4 Hats = 24 different combinations

Starting from Wednesday we have

W-T-F-Sa-Su-M-T = 7 days * 3 = 21 days (21st day will be Tuesday)

Next 3 remaining days : W - T - F

This means on Saturday combination will be repeated.

(D)

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Re: On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and   [#permalink] 10 Apr 2019, 22:48
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