Data Sufficiency

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?

(1) Exactly 3 of the integers are consecutive primes.

(2) The smallest integer is 3.

anusheelp wrote: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?

(1) Exactly 3 of the integers are consecutive primes.

(2) The smallest integer is 3.

Since the average of the 5 integers is 5, the sum of all 5 integers = 5*5 = 25.
After 2 integers are discarded, the average of the remaining 3 integers is 4, implying that the sum of the remaining 3 integers = 3*4 = 12.
Thus, the sum of the 2 discarded integers = 25-12 = 13.
Thus, the correct set of 5 integers must exhibit the following characteristics:
The integers are distinct and between 0 and 9, inclusive.
The sum of all 5 integers is 25.
The sum of 3 of the integers is 12.
The sum of the other 2 integers is 13.

Statement 1: Exactly 3 of the integers are consecutive primes.
Case 1: 2,3,5
Thus, the options for the remaining 2 integers are 0,1,4,6,8,9.
Since 2+3+5 = 10, the sum of the remaining 2 integers = 25-10 = 15.
Only one combination works: 6+9.
Thus, the 5 integers would be 2,3,5,6,9.
This list does not include two integers whose sum is 13.

Case 2: 3,5,7
Thus, the options for the remaining 2 integers are 0,1,4,6,8,9.
Since 3+5+7 = 15, the sum of the remaining 2 integers = 25-15 = 10.
Only two combinations work: 1+9 and 4+6.
Thus, the 5 integers are either 1,3,5,7,9 or 3,4,5,6,7.
Only the second option includes two integers with a sum of 13 (6+7=13).
Thus, the 5 integers are 3,4,5,6,7.
SUFFICIENT.

Statement 2: The smallest integer is 3.
We know from statement 1 that 3,4,5,6,7 works.
For the smallest integer to be 3, the sum of the remaining 4 integers must be 25-3 = 22.
Given that these remaining 4 integers must each be greater than 3, there are no options aside from 4+5+6+7 = 22.
Thus, the 5 integers are 3,4,5,6,7.
SUFFICIENT.

The correct answer is D.

The sum of the 5 distinct integers is 25.

The sum of the two number which were removed is 13.
Sum of remaining 3 numbers is 12.

1) Exactly 3 of the integers are consecutive primes.

Lets consider 3,5 and 7. Sum of these 3 are 15. Remaining is 10.

We can have 2 + 8 = 10 or 1 + 9 = 10 or even -2 + 12.

So not sufficient.

2) Smallest integer is 3.

Lets add the consecutive starting 3.

3+4+5+6+7 = 25

7 has to be the greatest number. If the greatest number is greater than 7 then the smallest number will become smaller than 3 which is against what is given in statement 2).

IMO [spoiler]B)[/spoiler]

Dear GMAT GURUNY

The integers are distinct and between 0 and 9, inclusive.

I am sorry but I do not understand why we should not consider negative numbers too.

Got it....silly one..

Thanks GMATGuruNY.

I arrived at the same result. However, the OA listed was A, so wanted an expert's response.