How much greater was the original price of the jacket...

[dianapaolasanchez]

The sales price of a certain jacket was15 percent less than its original price, and the sale price of a certain shirt was 10 percent less than original price. How much greater was the original price of the jacket than the original price of the shirt?
1) The sale price of the jacket was $83 greater than the sales price of the shirt
2) The original price of the jacket was $140

I think the aswer is C, because we have the original price of the jacket and the realtion between the sale price between the jacket and the shirt, but I am not sure. Can somebody explain me? Thank you

[mikrodj]

I think you're right. However, using "reasoning" is not the best way to solve hard problems. I believe this would have been a perfect problem for a C trap.

Consider
Sj = selling price of the jacket
Ss = selling price of the shirt
Oj = original price of the jacket
Os = original price of the shirt

Sj = 0.85 Oj
Ss = 0.9 Os

the rephrase of the question what is Oj - Os?

set the grid BD/ACE since second statement is easier

2) The original price of the jacket was $140
you have Oj but you don't have Os so eliminate B and D

1) The sale price of the jacket was $83 greater than the sales price of the shirt

Sj = Ss + 83 the information you have is Sj - Ss = 83. Since the percentages of the relations between the original prices are different this is insufficient.

As you said combining both statements answer is C.

However if you change statement I for this one

the sale price of 18 jackets was 200 dollars greater than the sales price of 17 shirts, answer would have been A

Sj = 0.85 Oj --> 100 Sj = 85 Oj --> (100/85)Sj = Oj ---> (20/17)Sj=Oj
Ss = 0.9 Os --> 100 Ss = 90 Os ---> (10/9)Ss = Oj ---

rephrase Oj - Os? ---> (20/17)Sj - (10/9)Ss ---> 180Sj -170Ss/(17*9) -->10*(18Sj-17Ss)/(17*9) --> final rephrase what is 18Sj - 17Ss

because with this new statement I we can answer that rephrase the answer would have been A.

Sorry for the long reply but I wanted to point out that sometimes using "reasoning" leads you to incorrect answer choices. This was not the case.

[RonPurewal]

@ mikrodj: good analysis, but that's FOUR variables. that's a lot of variables; usually, that's walking death, as far as time management is concerned, once you start to have that many variables in one problem.

all you need is two variables: J for the original price of the jacket, and S for the original price of the shirt.
then the sale prices are 0.85J and 0.8S, respectively.

so it's:
What is J - S ?
(1) 0.85J = 0.9S + 83
(2) J = 140

this is somewhat unusual, in that the correct answer is actually (c), which is the "naive guess" (just substitute #2 into #1).

--

of note, however, is the fact that, if both sales were the same % discount, then the answer would be (a), not (c).

for instance, let's say both sales are 15% off, rather than one 15% and one 10%.
in that case, statement (1) becomes 0.85J = 0.85S + 83, which can be rearranged to 0.85(J - S) = 83. in that case, we can isolate (J - S), so in that case (1) would be sufficient!

[mikrodj]

@ mikrodj: good analysis, but that's FOUR variables. that's a lot of variables; usually, that's walking death, as far as time management is concerned, once you start to have that many variables in one problem.

all you need is two variables: J for the original price of the jacket, and S for the original price of the shirt.
then the sale prices are 0.85J and 0.8S, respectively.

so it's:
What is J - S ?
(1) 0.85J = 0.9S + 83
(2) J = 140

this is somewhat unusual, in that the correct answer is actually (c), which is the "naive guess" (just substitute #2 into #1).

--

of note, however, is the fact that, if both sales were the same % discount, then the answer would be (a), not (c).

for instance, let's say both sales are 15% off, rather than one 15% and one 10%.
in that case, statement (1) becomes 0.85J = 0.85S + 83, which can be rearranged to 0.85(J - S) = 83. in that case, we can isolate (J - S), so in that case (1) would be sufficient!

Timing was always my problem :). When I took the test I spent four minutes with the first question and had to guess blindly the last three. I managed to score 50, but please don't do what I did.

[esledge]

Timing was always my problem :). When I took the test I spent four minutes with the first question and had to guess blindly the last three. I managed to score 50, but please don't do what I did.

Good advice!