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Bunuel
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On a meeting every person shook hands with every other person once. If 12 Mar 2021, 03:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

72% (01:34) correct 28% (02:02) wrong based on 98 sessions

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On a meeting every person shook hands with every other person once. If there were total of 91 handshakes, how many people were on the meeting?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
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C
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stne
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On a meeting every person shook hands with every other person once. If 24 Mar 2021, 06:46
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Bunuel
On a meeting every person shook hands with every other person once. If there were total of 91 handshakes, how many people were on the meeting?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Show more

Question can be expressed as \(n_{C_2}=91\) find the value of \(n\) ?

\(\frac{n!}{2! (n-2)!} = 91\)

\(n* (n-1) = 182\)

solving for \(n\)

\(n=14\)

Ans-C

hope it's clear.
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hk111
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On a meeting every person shook hands with every other person once. If 27 Mar 2021, 02:14
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stne
Bunuel
On a meeting every person shook hands with every other person once. If there were total of 91 handshakes, how many people were on the meeting?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

Question can be expressed as \(n_{C_2}=91\) find the value of \(n\) ?

\(\frac{n!}{2! (n-2)!} = 91\)

\(n* (n-1) = 182\)

solving for \(n\)

\(n=14\)

Ans-C

hope it's clear.
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Hi, Can you please elaborate your calculation?
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On a meeting every person shook hands with every other person once. If 27 Mar 2021, 08:22
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hk111
stne
Bunuel
On a meeting every person shook hands with every other person once. If there were total of 91 handshakes, how many people were on the meeting?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

Question can be expressed as \(n_{C_2}=91\) find the value of \(n\) ?

\(\frac{n!}{2! (n-2)!} = 91\)

\(n* (n-1) = 182\)

solving for \(n\)

\(n=14\)

Ans-C

hope it's clear.

Hi, Can you please elaborate your calculation?
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Hi hk111,

\(n_{C_2}=91\)

\(= \frac{n!}{2! (n-2)!} = \frac{n *(n-1)(n-2)!}{2! (n-2)!} = 91\)

Now cancel \(( n-2)!\) from numerator and denominator we are left with:

\(\frac{n *(n-1)}{2}=91 \)

\(n*(n-1) =182\)

Now to find \( n\) , just use the options .

Put the values of \(n \) from the options and see for which \(n\) we get \(n*(n-1) =182\)

You will see \(n = 14 \) satisfies

\(14 *13 = 182\)

Let me know if anything still remains unclear.

Thank you.
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On a meeting every person shook hands with every other person once. If 30 Mar 2021, 07:07
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Given
    • In a meeting, every person shook hands with every other person once.
To find
    • The number of people in the meeting if there were a total of 91 handshakes.

Approach and Working out

For 1 handshake, 2 people are needed.
So, total number of handshakes = total number of ways of selecting 2 people = nc2 = n(n-1)/2
    • n(n-1)/2 = 91
    • n(n-1) =182

\(n^2\) -n -182 =0
    • \(n^2\) -14n +13n -182 = 0
    • n(n-14) +13(n-14) = 0
    • (n-14)(n+13) = 0
    • n= 14, -13(We reject -13 as number of people cannot be negative)
      o n=14
Hence, option C is the correct answer.

Correct Answer: Option C
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