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The average of 5 distinct single digit integers is 5. If 2 [#permalink]
31 Oct 2007, 10:05

The average of 5 distinct single digit integers is 5. If 2 integers are discarded, the new average is 4. What is the largest of the 5 integers?

1) Exactly (no more than) 3 of the integers are consecutive primes.
2) The smallest integer is 3.

The answer is A. It is clear that there is only one combination of numbers that meet the requirements of 1). However, it seems to me that there is only one combination of numbers that meet 2) also: 3,4,5,6,7, where (3+4+5)/3 = 4. So wouldn't the answer be d?

For 1) the only possible combination of numbers that works is 3,4,5,6,7. Since there are exactly (no more than) 3 consecutive primes, 2,3,5,7 cannot be in the same batch of numbers. So for both 1 and 2 independent of each other, the only group of numbers that work are 3,4,5,6,7.