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At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party? A: 30 B: 12 C: 14 D: 25

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Use the sum of AP series concept, where Sn= 66, first term a1=1, common difference d=1, then find n. Putting all the values in the formula of Sn we get, n^2+n-132=0 Required answer= n+1 which will come to be 12 (OPTION B)
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If there are N people then there would be shakehands with N-1 people. N(N-1)/2 = 66 N^2 - N - 132=0 N=12 people in the party. Option B is the right answer.
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