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?
Henry's sale : DS problem... pls help
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From stat1: most exp.item = $15,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?
then from given info: 20%(15) + 10%( a + 20 ) > 15% ( 15 + a + 20)
=> 10%15 > 5% ( 35 + a ) => 1.5 > 1.75 + 5% of a.
irrespective of a's value, the above statement can be answered. which is NO.
Hence A!
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Hi praveen_gmat!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?
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
Whitney Garner
GMAT Instructor & Instructor Developer
Manhattan Prep
Contributor to Beat The GMAT!
Math is a lot like love - a simple idea that can easily get complicated
GMAT Instructor & Instructor Developer
Manhattan Prep
Contributor to Beat The GMAT!
Math is a lot like love - a simple idea that can easily get complicated