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A company bought some desks at a price of $150 each and some chairs at
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29 May 2012, 22:30
29 May 2012, 22:30
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A company bought some desks at a price of $150 each and some chairs at a price of $50 each. Did the company buy more than 40 chairs?
(1) The total price of the desks and chairs that the company bought was $5,000.
(2) The company bought fewer than 20 desks.
ID 12555
(1) The total price of the desks and chairs that the company bought was $5,000.
(2) The company bought fewer than 20 desks.
ID 12555
Can some experts explain a systematic approach for solving optimization type problems, I am usually lost as to where to start on such problems.
Please explain your approach by helping solve this problem from GMAtprep software. As many creative approaches as possible.
Thanks for your help
Kaps
Please explain your approach by helping solve this problem from GMAtprep software. As many creative approaches as possible.
Thanks for your help
Kaps
Re: A company bought some desks at a price of $150 each and some chairs at
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30 May 2012, 00:59
30 May 2012, 00:59
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Expert Reply
A company bought some desks at a price of $150 each and some chairs at a price of $50 each. Did the company buy more than 40 chairs?
(1) The total price of the desk and chairs is 5,000 --> \(150d+50c=5,000\) --> \(3d+c=100\). \(c\) can be more than 40 as well as less than or equal to 40. For example consider \(c=40\) and \(d=20\) for a NO answer and \(c=70\) and \(d=10\) for an YES answer. Not sufficient.
(2) The company bought fewer than 20 desks --> \(d<20\). Clearly insufficient.
(1)+(2) From (1) we have that \(3d+c=100\) and from (2) \(d<20\). Now, even if \(d=19\) (maximum possible value for \(d\)) the number of chairs bought would be: \(3*19+c=100\) --> \(c=43\), so still more than 40. Sufficient.
Answer: C.
Hope it's clear.
(1) The total price of the desk and chairs is 5,000 --> \(150d+50c=5,000\) --> \(3d+c=100\). \(c\) can be more than 40 as well as less than or equal to 40. For example consider \(c=40\) and \(d=20\) for a NO answer and \(c=70\) and \(d=10\) for an YES answer. Not sufficient.
(2) The company bought fewer than 20 desks --> \(d<20\). Clearly insufficient.
(1)+(2) From (1) we have that \(3d+c=100\) and from (2) \(d<20\). Now, even if \(d=19\) (maximum possible value for \(d\)) the number of chairs bought would be: \(3*19+c=100\) --> \(c=43\), so still more than 40. Sufficient.
Answer: C.
Hope it's clear.
General Discussion
Re: A company bought some desks at a price of $150 each and some chairs at
[#permalink]
30 May 2012, 00:23
30 May 2012, 00:23
Expert Reply
Let d be the price of a desk and c the price of a chair. We are to determine whether the company bought more than 40 chairs (i.e. whether it bought 41 or more chairs)
Using statement 1:
150d + 50c = 5,000
One possible solution to this equation is d=20, c=40. Another possible solution is d=18, c=46. In the first case, the company buys less than 41 chairs, in the second it buys more than 41 chairs. Insufficient.
Using statement 2:
In this case we do not know the total expenditure made. The number of chairs bought could have been more or less than 41. Insufficient.
Combining both statements:
If fewer than 20 desks were bought, and the total spent was $5,000, then for each possible solution the number of chairs will be >= 46. Therefore the number of chairs sold is greater than 41. Sufficient.
C it is.
Using statement 1:
150d + 50c = 5,000
One possible solution to this equation is d=20, c=40. Another possible solution is d=18, c=46. In the first case, the company buys less than 41 chairs, in the second it buys more than 41 chairs. Insufficient.
Using statement 2:
In this case we do not know the total expenditure made. The number of chairs bought could have been more or less than 41. Insufficient.
Combining both statements:
If fewer than 20 desks were bought, and the total spent was $5,000, then for each possible solution the number of chairs will be >= 46. Therefore the number of chairs sold is greater than 41. Sufficient.
C it is.
