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Brian's purchase

by Night reader » Wed Dec 22, 2010 12:53 am
Brian has forgotten how much money he had spent on the purchase of one computer and one software package. He remembers exactly that one computer cost him $50 less than the amount not exceeding 5 times the cost of one software package. He also remembers the average cost for two items was $700 and the software package cost between $250-350. How much Brian had spent for one computer?

A. 1000
B. 1050
C. 1100
D. 1150
E. 1200
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by Rahul@gurome » Wed Dec 22, 2010 1:51 am
Night reader wrote:Brian has forgotten how much money he had spent on the purchase of one computer and one software package. He remembers exactly that one computer cost him $50 less than the amount not exceeding 5 times the cost of one software package. He also remembers the average cost for two items was $700 and the software package cost between $250-350. How much Brian had spent for one computer?

A. 1000
B. 1050
C. 1100
D. 1150
E. 1200
Say price of computer = $C and price of software package = $S
Thus (C + S) = 700 => (C + S) = 1400 => S = (1400 - C)
Now S lies between 250 and 350 => (1400 - C) lies between 250 and 350
=> C lies between 1050 and 1150

Only such option is 1100.

The correct answer is C.
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by fskilnik@GMATH » Wed Dec 22, 2010 11:36 am
Rahul@gurome wrote:Say price of computer = $C and price of software package = $S
Thus (C + S) = 2*700 => (C + S) = 1400 => S = (1400 - C)
Now S lies between 250 and 350 => (1400 - C) lies between 250 and 350
=> C lies between 1050 and 1150, both extremities allowed!
Only such option is 1100. Nope...and there was another question stem info to be used!
From the question stem, although it is very bad-wording, we know that C+50 = A < 5(1400-C) where A is the greatest amount possible!!

Solving the inequality C+50 < 5(1400-C) we get C< 1158.33 therefore I guess we should use C = 1150, because it is the upper limit of the interval [1050, 1150] already found (as Rahul calculated).

Please note that in this case we would get C+50 = 1200 = A and 1200 is in fact less than 5(1400-1150) = 5*250 = 1250...

Therefore I believe the correct answer is D.

Regards,
Fabio.
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by Rahul@gurome » Wed Dec 22, 2010 12:19 pm
Thanks for this detailed analysis fskilnik!
But I personally believe "the software package cost between $250-350" means the price lies between $250 and $300. That's why I ignored the another information. Anyway I agree with your solution and also on the "bad wording" point.
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by fskilnik@GMATH » Wed Dec 22, 2010 12:31 pm
Rahul@gurome wrote:Thanks for this detailed analysis fskilnik!
But I personally believe "the software package cost between $250-350" means the price lies between $250 and $300. That's why I ignored the another information. Anyway I agree with your solution and also on the "bad wording" point.
Hi Rahul!

The word "between" is really (always) "problematic", for sure. I prefer to consider x between a<b as "a <= x <= b" but this is just a matter of taste, for sure*.

In this problem, I´ve decided to look for the info you´ve ignored exactly because I could not understand it at first, too. And, as you agree on the "(very) bad wording", I simply "guessed" what we "should" infer from what was written... bad, bad, bad, although the idea behind the problem was a nice one, for sure.

Best Regards,
Fabio.

P.S.: beautiful solution of yours for the triplets. Beautiful. It was a pleasure for me to explain it for the "audience". Cheers!

(*) For other readers: do not worry about that in the official GMAT test, because this will never be an issue... if it makes a difference in a certain GMAT problem, the examiner will use the word "inclusive" or "exclusive".
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