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There are 10 students in a class. A student is allowed to shake hand o

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nick1816
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There are 10 students in a class. A student is allowed to shake hand o [#permalink] New post   27 Jun 2019, 17:32
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There are 10 students in a class. A student is allowed to shake hand only once with a student who is taller than him or equal in height to him. He can’t shake hand with anyone who is shorter than him. Average height of the class is 5 feet. What is the difference between the maximum and minimum number of handshakes that can take place in the class?

A. 20
B. 25
C. 30
D. 35
E. 45
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There are 10 students in a class. A student is allowed to shake hand o [#permalink] New post   28 Jun 2019, 01:31
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nick1816 wrote:
There are 10 students in a class. A student is allowed to shake hand only once with a student who is taller than him or equal in height to him. He can’t shake hand with anyone who is shorter than him. Average height of the class is 5 feet. What is the difference between the maximum and minimum number of handshakes that can take place in the class?

A. 20
B. 25
C. 30
D. 35
E. 45

Maximum number of handshakes = when all students are of the same height (they can all shake hands with each other, without any restriction on anybody) = 10C2 = 45

Minimum number of handshakes = when all students are of different heights (no one can shake hands with anyone (please forgive me for the SC error, if any) since it's stated that there is a constraint that no taller student can shake hands with a shorter student, so if no one is equal in height, of any pair of boys we choose to shake hands with each other - one will be taller / shorter than the other, which prohibits them from shaking hands) = 0

Answer = Maximum - Minimum = 45-0 = 45 (E)

Simple and short :)
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Lampard42
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Re: There are 10 students in a class. A student is allowed to shake hand o [#permalink] New post   28 Jun 2019, 01:55
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nick1816 wrote:
There are 10 students in a class. A student is allowed to shake hand only once with a student who is taller than him or equal in height to him. He can’t shake hand with anyone who is shorter than him. Average height of the class is 5 feet. What is the difference between the maximum and minimum number of handshakes that can take place in the class?

A. 20
B. 25
C. 30
D. 35
E. 45


Good trap question.
Maximum is when all are 5 feet= 10C2=45
Minimum is when all are of different height then 0 shakes cause the shorter person cannot shake hands with a taller guy as he will be shorter to the taller guy ( didn’t realize it and arrived at 45 shakes here too and wasted time)

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Re: There are 10 students in a class. A student is allowed to shake hand o [#permalink]
28 Jun 2019, 01:55
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