Data Sufficiency

praveen_gmat wrote:Henry purchased 3 items during a sale. He received a 20 percent discount of the regular price of the most
expensive item and a 10 percent discount off the regular price of the other 2 items. Was the total amount of
the 3 discounts greater than 15 percent of the sum of regular prices of the 3 items?
(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive
item was $20.
(2) The regular price of the least expensive item was $15

Well the popular answer is A, and some threads in btg state that the explanation. I have only one question.

How can the "other 2 items" be same as "next most expensive" item?

Hi praveen_gmat!

A good way to start would be to rephrase this question, so let's get some variables:

E = most expensive item
M = middle priced item
L = lowest priced item

The question asks if 20% of E and 10% of M and L is greater than 15% of the sum E+M+L.

Is .2E + .1(M+L) > .15(E+M+L)?

So let's multiply this out and clean things up a bit:

.2E + .1M + .1L > .15E + .15M + .15L? (group like terms)
.05E > .05M + .05L?
E > M + L?

Statement (1):
This tells us that E=$50 and that M=$20, so the question becomes "Is 50 > 20 + L?"

This might seem insufficient, but we know that L is the lowest price and therefore less than $20. So, is $50 less than $20 + some amount less than $20? So let's think of the extreme, if the lowest price was $19.99, then the answer is YES... $50 is more than $20+$19.99. Sufficient.

Statement (2):
This tells us that L=$15, so the question becomes "Is E > M + 15?" We know that both E and M are larger than $15, but we have NO CLUE anything more than that. Insufficient.

The correct answer is A.


Whit