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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.

The constituency in which B got lower number of votes compared to A and C is
  1. S3
  2. S4
  3. S2
  4. S1

Answer and explanation

Correct answer: C - S2
Unique consistent allocation (A,B,C): S1 (19,1,0), S2 (7,5,8), S3 (6,6,8), S4 (9,11,0), S5 (8,12,0). [C must win S2,S3 with >=7 each but total only 16; B wins S4,S5; B votes increasing summing to 35.] Only in S2 does B (5) get fewer votes than both A (7) and C (8).

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  • IPMAT Indore

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