What is the average of a set of 6 consecutive odd integers ?

Question

(1) The sum of two numbers of the set is 40
(2) The sum of two numbers of the set is 24

BrushMyQuant · Answer

We need to find what is the average of a set of 6 consecutive odd integers

STAT 1 : The sum of two numbers of the set is 40 
Let one number be x and other be x + 2
=> x + x + 2 = 40
=> 2x = 40 - 2 = 38
=> x =  \frac{38}{2}  = 19
=> Numbers are 19 and 21.
But we don't know if other numbers are greater than these numbers or smaller
=>   NOT SUFFICIENT

STAT 2 : The sum of two numbers of the set is 24 
Let one number be y and other be y + 2
=> y + y + 2 = 24
=> 2y = 24 - 2 = 22
=> y =  \frac{22}{2}  = 11
=> Numbers are 11 and 13
But we don't know if other numbers are greater than these numbers or smaller
=>   NOT SUFFICIENT

Combining Both the statements  we get 
Numbers are 11, 13, 19, 21
So, other numbers will be 15 and 17
=> Average will be the average of middle two terms =  \frac{15+17}{2}  = 16
=>   SUFFICIENT

So,  Answer will be C 
Hope it helps!

Watch the following video to learn How to Sequence problems

https://www.youtube.com/watch?v=EfNT2JoE5CM

ahujajanvi08 · Answer

is doesn't specify anywhere that the two numbers are consecutive it can be the sum of first and last number also? can you explain

Bunuel · Answer

What is the average of a set of 6 consecutive odd integers ?

Assume that the six consecutive  odd  integers are x, x + 2, x + 4, x + 6, x + 8, and x + 10.

(1) The sum of two numbers of the set is 40

To get the smallest possible value of x for which this is possible in our set, assume that the two largest numbers, x + 8 and x + 10, add up to 40. Then x + 8 + x + 10 = 40, which gives x = 11.

So, the set can be {11, 13, 15, 17, 19, 21}, where the two largest numbers, 19 and 21, sum to 40.

To maximize x, assume that the two smallest numbers, x and x + 2, add up to 40. Then x + x + 2 = 40, which gives x = 19.

In this case the set is {19, 21, 23, 25, 27, 29}, and the sum of the first two numbers, 19 and 21, is 40.

These two possible sets give different totals, and therefore different averages. No6t sufficient.

Other valid sets also exist, for example: 
{13, 15, 17, 19, 21, 23}
{15, 17, 19, 21, 23, 25}
{17, 19, 21, 23, 25, 27}

(2) The sum of two numbers of the set is 24

Similarly, to get the smallest possible value of x for which this is possible in our set, assume that the two largest numbers, x + 8 and x + 10, add up to 24. Then x + 8 + x + 10 = 24, which gives x = 3.

So, the set can be {3, 5, 7, 9, 11, 13}, where the two largest numbers, 11 and 13, sum to 24.

To maximize x, assume that the two smallest numbers, x and x + 2, add up to 24. Then x + x + 2 = 24, which gives x = 11.

In this case the set is {11, 13, 15, 17, 19, 21}, and the sum of the first two numbers, 11 and 13, is 24.

These two possible sets give different totals, and therefore different averages. Not sufficient.

Other valid sets also exist, for example:
{5, 7, 9, 11, 13, 15}
{7, 9, 11, 13, 15, 17}
{9, 11, 13, 15, 17, 19}

(1)+(2) The only set that satisfies both conditions is {11, 13, 15, 17, 19, 21}. Therefore, the set is fixed, and we can find its average. Sufficient.

Answer: C.

Yes, that solution is not precise. Check the above one.

What is the average of a set of 6 consecutive odd integers ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What is the average of a set of 6 consecutive odd integers ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards