Data Sufficiency

jjjinapinch wrote:Did the sum of the prices of three shirts exceed $60?
(1) The price of the most expensive of the shirts exceeded $30.
(2) The price of the least expensive of the shirts exceeded $20.

Official Guide question
Answer: B

Target question: Did the sum of the prices of three shirts exceed $60?

Statement 1: The price of the most expensive of the shirts exceeded $30
This statement doesn't FEEL sufficient, so I'll TEST some values.
Case a: the shirt prices are $31, $32 and $33, in which case the sum of the 3 prices EXCEEDS $60
Case b: the shirt prices are $11, $12 and $33, in which case the sum of the 3 prices DOES NOT exceed $60
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: The price of the least expensive of the shirts exceeded $20
If the least expensive shirt costs 20+ dollars, then the other 2 shirts also cost 20+ dollars each
(20+ dollars) + (20+ dollars) + (20+ dollars) = 60+ dollars
So, we can conclude that the sum of the 3 prices EXCEEDS $60
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

jjjinapinch wrote:Did the sum of the prices of three shirts exceed $60?
(1) The price of the most expensive of the shirts exceeded $30.
(2) The price of the least expensive of the shirts exceeded $20.

We must determine whether the price of 3 shirts exceeded $60.

Statement One Alone:

The price of the most expensive of the shirts exceeded $30.

Without knowing the price of at least one of the other two shirts, we do not have enough information to answer the question. For example, the most expensive shirt could be $31 and the two less-expensive shirts could be $1 each, and thus the price of the 3 shirts would be less than $60. However, the most expensive shirt could be $50 and the two less-expensive shirts could be $10 each; then, the total price would exceed $60.

Statement Two Alone:

The price of the least expensive of the shirts exceeded $20.

We have enough information to determine that the price of the three shirts exceeded $60. We know that price of the least expensive shirt is greater than $20, and furthermore we know that the price of any one of the other two shirts has to be greater than the least expensive shirt. Thus, no matter what the prices of the three shirts are, the sum will always be greater than $60. Statement two is sufficient to answer the question.

Answer: B