The average of 5 distinct single digit integers is 5. If 2

Question

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?

Thanks

jimjohn · Answer

take 2,3,5,7,8
their average is 5.
now if i take out 8 and 5 from these
im left with 2,3,7 and their average is 4.
the smallest integer was 2, not 3

jimjohn · Answer

wait a second but doesnt this make A wrong too then? was A the OA?

jimjohn · Answer

or actually wait 8 is still the largest number in both cases.

baileyf16 · Answer

The OA is A. 

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. 

So why is the answer not d?

jimjohn · Answer

ok my bad i see it now. D does make sense to me, can anyone else figure out why D is not right?

The average of 5 distinct single digit integers is 5. If 2

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