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

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.

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.

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.

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.