Data Sufficiency

The average (arithmetic mean) of integers r,s,t,u,v is 100. Are exactly two integers greater than 100?

(1) Three of the integers are less than 50

(2) None of the integers are equal to 100.


thanks.

(1) Since 3 of the numbers are less than 50 we know that only 1 is greater than 100. So the answer to the question is no. This is sufficient.

(2) Consider 99, 99, 101, 101. Exactly two numbers are greater than 100 and the mean is 100. Now consider 50, 50, 50, 250. Only one number is greater than 100 and the mean is 100. This is insufficient.

The answer is A.

The princeton review book begs to differ, the answer there is E!! (altho i came up with A also)

Princeton Review is definitely wrong. It's unfortunate that Kaplan and Princeton Review books aren't edited like the OG.

raleigh wrote:(1) Since 3 of the numbers are less than 50 we know that only 1 is greater than 100. So the answer to the question is no. This is sufficient.

(2) Consider 99, 99, 101, 101. Exactly two numbers are greater than 100 and the mean is 100. Now consider 50, 50, 50, 250. Only one number is greater than 100 and the mean is 100. This is insufficient.

The answer is A.

you miss quoted the second statement. its 5 variables and you are showing 4 variables...!! The sum of all the numbers is 500 according to the stem info in the question.

(1) Consider 25, 25, 25, 125, 300. The mean is 100, and exactly 2 integers is greater than 100.

Now consider 25, 25, 125, 125, 200. The mean is 100, and 3 integers are greater than 100.

This is insufficient.

(2) Note that none of the numbers that we selected for (1) are equal to 100. Apply those choices here, and this is insufficient.

(1)+(2) Select the same numbers that showed (1) and (2) insufficient and this is also insufficient.

The answer is E. Good catch. Sorry for the mistake.

Thanks raliegh! helped clear my doubt.