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# If 11 persons meet at a reunion and each person shakes hands exactly o

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Math Expert
Joined: 02 Sep 2009
Posts: 58989
If 11 persons meet at a reunion and each person shakes hands exactly o  [#permalink]

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08 Dec 2014, 06:26
00:00

Difficulty:

25% (medium)

Question Stats:

61% (00:47) correct 39% (00:54) wrong based on 185 sessions

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Tough and Tricky questions: Combinations.

If 11 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?

A) 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
B) 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
C) 11 × 10
D) 55
E) 45

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: If 11 persons meet at a reunion and each person shakes hands exactly o  [#permalink]

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08 Dec 2014, 06:29
1
11C2 = 11*10/2 = 11*5 = 55
Ans - D
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Re: If 11 persons meet at a reunion and each person shakes hands exactly o  [#permalink]

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08 Dec 2014, 07:06
1
If 11 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?

A) 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
B) 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
C) 11 × 10
D) 55
E) 45

Total number of handshakes = $$C^{11}_{2}$$$$= \frac{11*10}{2}=55$$

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Joined: 02 Sep 2009
Posts: 58989
Re: If 11 persons meet at a reunion and each person shakes hands exactly o  [#permalink]

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09 Dec 2014, 06:51
Bunuel wrote:

Tough and Tricky questions: Combinations.

If 11 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?

A) 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
B) 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
C) 11 × 10
D) 55
E) 45

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: If 11 persons meet at a reunion and each person shakes hands exactly o  [#permalink]

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09 Dec 2014, 07:00
2
If 11 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?

1st person will have 10 handshakes, 2nd will have 9, ....10th will have 1 and 11th will have 0
= 10+9+8+7+6+5+4+3+2+1 = 55

if we generalize this: if there are n people then there will be n(n-1)/2 handshakes.

Ans.D) 55
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Re: If 11 persons meet at a reunion and each person shakes hands exactly o  [#permalink]

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19 Oct 2015, 11:05
JJo wrote:
If 11 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?

1st person will have 10 handshakes, 2nd will have 9, ....10th will have 1 and 11th will have 0
= 10+9+8+7+6+5+4+3+2+1 = 55

if we generalize this: if there are n people then there will be n(n-1)/2 handshakes.

Ans.D) 55

JJo I think you meant n(n+1)/2 handshakes.
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Re: If 11 persons meet at a reunion and each person shakes hands exactly o  [#permalink]

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19 Oct 2015, 11:44
1
2
Hi All,

This question doesn't require any special math formulas - you just need to take some notes and do a bit of arithmetic.

We're told that 11 people will each shake hands with one another. We're asked how many handshakes actually occur:

I'm going to name the 11 people ABCDE FGHIJ and K

A shakes the hands of the 10 other people.
B has ALREADY shook hands with A, so B shakes 9 'new' hands.
C has ALREADY shook hands with A and B, so C shakes 8 'new hands.
Etc.

You should notice that with each new person, the number of 'new' handshakes decreases by 1. This gives us...

10+9+8+7+6+5+4+3+2+1+0

For a total of 55

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Re: If 11 persons meet at a reunion and each person shakes hands exactly o  [#permalink]

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21 Oct 2015, 17:59
Bunuel wrote:

Tough and Tricky questions: Combinations.

If 11 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?

A) 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
B) 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
C) 11 × 10
D) 55
E) 45

Kudos for a correct solution.

Source: Chili Hot GMAT

its the sum from 1 to 10, coz the person can't shake hands with himself then each next to him loses 1 chance to shake hands because he's shaken hands with the one counted:

10+9+8+......+1=(10+1)*10/2=55

this shortcut applies to other questions the like, such as games between two teams blablabla
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Re: If 11 persons meet at a reunion and each person shakes hands exactly o  [#permalink]

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23 Mar 2016, 08:00
santorasantu : This can be made simple. Derive your own formula wherever needed.
Case 1.Two men would need only a single hand shake.
Case 2.Three men would need three hand shakes.
Your formula must satisfy above two cases.
Hence it is n(n-1)/2.
Case 1. 2*1/2 = 1
Case 2. 3*2/2 = 3

Our case : 11*10/2 = 55 . Answer is (D).
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Re: If 11 persons meet at a reunion and each person shakes hands exactly o  [#permalink]

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18 May 2019, 23:23
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Re: If 11 persons meet at a reunion and each person shakes hands exactly o   [#permalink] 18 May 2019, 23:23
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