Data Sufficiency Pack 1, Question 1) Is the average...

The question asks whether the average of 10 distinct integers > 20 ---> Sum of the 10 distinct integers > 200?

Per statement 1, if the smallest even integer of the set = 14, then we can definitely create the whole set and get a unique value (whether the sum is > or <200 is not relevant). Thus this statement is sufficient.

Per statement 2, sum \(\geq\)220 --> the average must be \(\geq\) 22. Thus sufficient.

D is the correct answer.
_________________

A) Positive EVEN distinct - smallest being 14.

So minimum average would be : 23 which is > 20.

B) Sum is at least 220... so average is at lease 22. which is > 20

Ans : D

It's really a nice question . EMPOWERgmatRichC



Question asks whether the Average of 10 integers is > 20 ?

Statement 1 says each integers are positive Even integers with 14 as smallest integer.
So the average would be at least 23 [average of 5th & 6th term of 14+16+18+20+22+ 24 ..... ] Sufficient.

Statement 2 says Sum of 10 integer is >= 220. So the average is >= 22. Sufficient.

Option (D) wins.

Is the average (arithmetic mean) of 10 distinct integers greater than 20?

(1) Each of the integers is a positive even number and the smallest is 14.
(2) The sum of the integers is at least 220.

average (arithmetic mean) of 10 distinct integers greater than 20 --- means the sum of all the distinct integer will greater that 200 .
sum of 10 distinct integers > 200

st 1 -->
smallest is 14 .
as it given that all the integer are distinct --- if we assign minimum value to all the 9 remaining integer
then it would be --- 15,16,17,18,19,20,21,22,23
then the overall sum will be less than 200 .

But we use any other integer keeping 14 as the least .Then we can have a sum >200

hence two different ans ..not sufficient

st 2 -->The sum of the integers is at least 220.
directly given that sum is at least 220 .
We only require to know whether the sum is greater than 200
hence sufficient .

Ans is B
_________________

Your interpretation of statement 1 is not correct. It is mentioned that the elements of the set are all EVEN distinct integers. Thus ruling 1 of your 2 cases out. Making this statement sufficient.
_________________

Hi All,

The prompt tells us that we're dealing with 10 DISTINCT Integers (meaning that there are 10 different numbers involved. We're asked if the AVERAGE of those 10 numbers is greater than 20. Since the average of a group of numbers = (sum of the numbers)/(number of terms), the question is ultimately asking if the SUM of the 10 distinct numbers is greater than 200. This is a YES/NO question.

1) Each of the integers is a positive even number and the smallest is 14.

This Fact tells us that all 10 numbers are EVEN and that the SMALLEST is 14. Since the prompt tells us that they are DISTINCT, then we can 'map out' the minimum possible set of values and see what the result is. That set would be...

14, 16, 18, 20, 22
24, 26, 28, 30, 32

The sum of those terms = 240 at the MINIMUM (you can calculate that sum in a variety of ways). Since any other possible sum will be GREATER than 240, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) The sum of the integers is at least 220.

This Fact gives us a minimum value for the SUM. Since the prompt is ultimately asking if the sum is greater than 200, no extra work is required here. The sum will ALWAYS be greater than 200.
Fact 2 is SUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

nice.. i missed the 'even' part.