The average of 6 distinct single-digit positive integers in a set is 4

Question

The average of 6 distinct single-digit positive integers in a set is 4. What is the greatest of these integers?
(1) 8 is a part of the set.
(2) 5 is not a part of the set.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

rajatchopra1994 · Answer

Explanation:

As average is 4, so total will be 6X4 = 24

Statement 1: 8 is a part of the set.
then, for the rest of 5 distinct numbers, the sum should be less than 16. that is possible. But if we take 9, sum 16 wont be possible.

So Sufficient.

Statement 2:5 not a part of set.
we want sum 24,as 5 is not there. let 8 is highest number. so from 1+2+3+4+6 =16 Possible
With 7 as highest not possible, same with 9.

So Sufficient.

IMO-D

ajaygaur319 · Answer

Isn't statement 2 redundant because there cannot be a set where 5 is the part of that set. There only exists one set: {1, 2, 3, 4, 6, 8}

rajatchopra1994 · Answer

Dear  ajaygaur319  ,

FOR DS Question, Individual statements can lead to answer. So in Statement 2, as 5 not part of the set.
1,2,3,4,6,8 is the only set, and 8 is being the highest number in the set which is providing an answer to the question. Statement 2 leads to the answer. That's why it is sufficient.

I hope, I had clarified your doubt. Any doubts, please do DM me. We can discuss this in the message.

Regards!!

nick1816 · Answer

ajaygaur319

There are 3 sets possible

1. {1,2,3,4,5,9}
2. {1,2,3,4,6,8}
3. {1,2,3,5,6,7}

Both statements lead to the 2nd one.

D

fireagablast · Answer

There's actually three sets
{1, 2, 3, 4, 6, 8}
{1, 2, 3, 4, 5, 9}
{1, 2, 3, 5, 6, 7}

Statements A and B both eliminate the latter two sets.

kimshi78 · Answer

Any tips to find the possible sets (quickly)?

The average of 6 distinct single-digit positive integers in a set is 4

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GMAT Data Sufficiency (DS) Questions

The average of 6 distinct single-digit positive integers in a set is 4

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