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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...

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by BTGmoderatorLU » Thu Nov 19, 2020 10:29 am
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Source: Magoosh

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

The OA is E
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Re: On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each...

by swerve » Thu Nov 19, 2020 3:57 pm
BTGmoderatorLU wrote: ↑
Thu Nov 19, 2020 10:29 am
 Source: Magoosh

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

The OA is E
\(3\) Shirts \(\cdot 2\) Sweaters \(\cdot 4\) Hats \(= 24\) different combinations

Starting from Wednesday we have

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

Next \(3\) remaining days: W - T - F

This means on Saturday combination will be repeated.

Therefore, D
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Re: On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each...

by Scott@TargetTestPrep » Wed Nov 25, 2020 8:23 am
BTGmoderatorLU wrote: ↑
Thu Nov 19, 2020 10:29 am
 Source: Magoosh

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

The OA is E
Solution:

There are 3 x 2 x 4 = 24 different combinations of outfits. Since he starts to wear the first combination on Wednesday, he will wear the 8th, 15th and 22nd combinations on subsequent Wednesdays. So he will wear the 23rd on Thursday and the 24th on Friday. Therefore, we see that he can no longer wear a different outfit on Saturday since he has exhausted all 24 combinations of outfits on Friday.

Answer: E

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