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09 Mar 2011, 15:12
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D
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Difficulty:
15%
(low)
Question Stats:
72% (00:45) correct
28%
(00:47)
wrong
based on 2381
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If 10 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) 10•9•8•7•6•5•4•3•2•1
(B) 10•10
(C) 10•9
(D) 45
(E) 36
(A) 10•9•8•7•6•5•4•3•2•1
(B) 10•10
(C) 10•9
(D) 45
(E) 36
09 Mar 2011, 15:20
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banksy
The total number of handshakes will be equal to the number of different pairs possible from these 10 people (one handshake per pair), so \(C^2_{10}=45\).
Answer: D.
20 Mar 2018, 11:46
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Hi All,
This question can be solved in a couple of ways: a high-concept math approach or a "brute-force" answer that anyone can use. I'll focus on the second method.
Since we have 10 people, who will all shake hands with one another, we know that each pair of people will lead to 1 hand shake (and a person CAN'T shake hands with himself or herself).
If we call the people ABCDE FGHIJ
Person A will shake hands with BCDE FGHIJ = 9 shakes
Person B ALREADY shook hands with A, so they won't shake hands again….
Person B will shake hands with CDE FGHIJ = 8 shakes
Person C ALREADY shook hands with A and B, so they won't shake hands again….
Person C will shake hands with DE FGHIJ = 7 shakes
Notice the pattern 9, 8, 7…..the numbers will shrink by 1 with every letter, so we'll end up with…
9+8+7+6+5+4+3+2+1+0 = 45 total handshakes.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This question can be solved in a couple of ways: a high-concept math approach or a "brute-force" answer that anyone can use. I'll focus on the second method.
Since we have 10 people, who will all shake hands with one another, we know that each pair of people will lead to 1 hand shake (and a person CAN'T shake hands with himself or herself).
If we call the people ABCDE FGHIJ
Person A will shake hands with BCDE FGHIJ = 9 shakes
Person B ALREADY shook hands with A, so they won't shake hands again….
Person B will shake hands with CDE FGHIJ = 8 shakes
Person C ALREADY shook hands with A and B, so they won't shake hands again….
Person C will shake hands with DE FGHIJ = 7 shakes
Notice the pattern 9, 8, 7…..the numbers will shrink by 1 with every letter, so we'll end up with…
9+8+7+6+5+4+3+2+1+0 = 45 total handshakes.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
