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In an election there were five constituencies S1, S2, S3, S4 and S5 with 20 voters each all of whom voted. Three parties A, B and C contested the elections. The party that gets maximum number of…

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In an election there were five constituencies S1, S2, S3, S4 and S5 with 20 voters each all of whom voted. Three parties A, B and C contested the elections. The party that gets maximum number of votes in a constituency wins that seat. In every constituency there was a clear winner. The following additional information is available:

- Total number of votes obtained by A, B and C across all constituencies are 49, 35 and 16 respectively
- S2 and S3 were won by C while A won only S1.
- Number of votes obtained by B in S1, S2, S3, S4 and S5 are distinct natural numbers in increasing order.

Assume that A and C had formed an alliance and any voter who voted for either A or C would have voted for this alliance. Then the number of seats this alliance would have won is
  1. 4
  2. 2
  3. 3
  4. 5

Answer and explanation

Correct answer: C - 3

C won S2 and S3 with only 16 votes in all. A winning count of 7 would leave 13 votes for A and B, so one of them would have at least 7 and C would not be a clear winner; hence C had exactly 8 in S2 and in S3 and none elsewhere. B's counts rise strictly and total 35: B is below 8 in S2 and S3 (so at least 5 and 6 there) and won S4 and S5 (so at least 11 and 12), which forces B = 1, 5, 6, 11, 12 and A = 19, 7, 6, 9, 8 (total 49). A and C together would have 19, 15 and 14 in S1, S2 and S3, beating B each time, but only 9 against 11 in S4 and 8 against 12 in S5. The alliance would win 3 seats.

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  • IPMAT Indore

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