Correct answer must be D, not A.

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

From the stem:
The sum of 5 distinct single digit integers is 5*5=25;
The sum of 3 of the integers is 3*4=12;
The sum of the other 2 of the integers is 25-12=13.

(1) Exactly 3 of the integers are consecutive primes. We can have two cases:

Case 1
The three consecutive primes are: 2, 3 and 5 --> 2+3+5=10.
The remaining 2 integers could be: 0, 1, 4, 6, 8 or 9 (notice that neither of the remaining 2 integer can be 7, since in this case we would have 4 consecutive primes, not 3). The sum of these two integers must be 25-10=15. From the list, only two integers whose sum is 15 are 6 and 9 (6+9=15).
Now, in this case the 5 integers would be {2, 3, 5, 6, 9}, but no 2 integers from the list give the sum of 13, thus the case when 3 consecutive primes are 2, 3 and 5 is not possible.

Case 2
The three consecutive primes are: 3, 5, and 7 --> 3+5+7=15.
The remaining 2 integers could be: 0, 1, 4, 6, 8 or 9 (notice that neither of the remaining 2 integer can be 2, since in this case we would have 4 consecutive primes, not 3). The sum of these two integers must be 25-15=10. From the list, there are two pairs of integers whose sum is 10: (1, 9) and (4, 6).
Now, in this case the 5 integers would be {1, 3, 5, 7, 9} or {3, 4, 5, 6, 7}. From the first list there are no 2 integers whose sum is 13. In the second list, such two integers are 6 and 7.

Hence, the 5 integers are {3, 4, 5, 6, 7}. Sufficient.

(2) The smallest integer is 3. The sum of the other 4 integers, each of which must be greater than 3, must be 25-3=22. Only 4+5+6+7=22 is possible (the sum of any other 4 integers will be more than 22), so the 5 integers are {3, 4, 5, 6, 7}. Sufficient.

Answer: D.

Hope it's clear.
_________________

The question does not mention that the integers are positive. What about the case where integers are negative?

Single digit integers mean integers from 0 till 9, inclusive.
_________________

Oops! Missed that part. Thanks for clarifying

Somehow I did not pay attention to the word "exactly" and that is why considered 2,3,5,7 a valid answer.

Couldn't it still be 7 though, even though the hint tells you there's 3 consecutive primes...even with 7, you could still have 3 consecutive. Granted there would be 4 in a row, but WITHIN that series of 4, there are two different ways to have 3 consecutive primes. Or does the GMAT not play 'tricks' like that?

I guess you are talking about case 1 in the first statement. Please be more specific when asking a question.

Now, if there is 7 and 4 then the set is {x, 2, 3, 4, 5, 7}. Ask yourself: how many consecutive primes are there?
_________________

What about 2+3+5+11+4=25, it has 4 primes but 3 consecutive primes??

The average of 5 distinct single digit integers is 5.

11 is NOT a single digit integer.
_________________

I'm confused about part (1)

I get 2,3,5,6,9
AND 1,3,5,7,9

Both of which average to 25, and can remove two numbers to average 4. The only issue I can see is that it doesn't follow "three consecutive prime numbers" to which I would say I don't have three consecutive primes. The first set everyone I'm sure agrees with, the second set 1,3,5,7 aren't consecutive primes because there is a 2 between 1 and 3. I would be frustrated if someone said the second set is NOT "consecutive primes" because then that would mean i got this problem wrong because of a vague interpretation of what "consecutive primes" means.

What is tested is whether you are able to figure out the solution by considering all the conditions given.

Statement 1:

The three consecutive primes could be, 2, 3,5. The remaining numbers can only be 6 and 9. But we need three numbers that add up to 13 which we do not have in this case. Condition not satisfied.

The other possibility is the three consecutive primes could be 3,5 and 7. Then the other two numbers are 4 and 6. This satisfies all the conditions. So sufficient

Statement 2:

The least of all is 3. The remaining 4 numbers should add up to 22 and satisfy the other conditions. The numbers can only be 4,5,6,7. So sufficient.

Answer D.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________