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A company bought some desks at a price of $150 each and some

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A company bought some desks at a price of $150 each and some  [#permalink]

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New post 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 desk and chairs is 5,000
(2) The company bought fewer than 20 desks

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

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Re: NEW GMATPREP 2.1- OPTIMIZATION PROBLEM CAN SOME EXPERTS HELP  [#permalink]

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New post 30 May 2012, 00:23
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.
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Re: A company bought some desks at a price of $150 each and some  [#permalink]

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New post 30 May 2012, 00:59
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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 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.
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Re: A company bought some desks at a price of $150 each and some  [#permalink]

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New post 01 Jun 2012, 03:28
Hi Bunuel,

Can you please explain what is wrong in having following generalization?

If initial ratio of price of desk:chair is 3:1 then total money spent (in case of option A it is 5000) must also be divided in the same ratio. Therefore ratio of cost of desk: cost of chair is 3750:1250 => 3:1. If each chair cost $50 then total chairs bought must be 1250/50 => 25.

Isn't this information enough to answer the question?

Awaiting your reply.

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Re: A company bought some desks at a price of $150 each and some  [#permalink]

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New post 01 Jun 2012, 03:45
mokap25 wrote:
Can some experts explain a systematic approach for solving optimization type problems, I am usually lost as to where to start on such problems.


Well this is a Yes/No DS question, and hence one should start solving the question to prove that both the answers are true i.e. "Yes" and a "No" and hence narrowing down to the solution
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Re: A company bought some desks at a price of $150 each and some  [#permalink]

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New post 01 Jun 2012, 07:55
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Ameya85 wrote:
Hi Bunuel,

Can you please explain what is wrong in having following generalization?

If initial ratio of price of desk:chair is 3:1 then total money spent (in case of option A it is 5000) must also be divided in the same ratio. Therefore ratio of cost of desk: cost of chair is 3750:1250 => 3:1. If each chair cost $50 then total chairs bought must be 1250/50 => 25.

Isn't this information enough to answer the question?

Awaiting your reply.

AMeya


The red part is not correct. The fact that the prices are in ratio 3 to 1, does not necessarily mean that the total amount spent would also be in the same ratio. For example consider \(d=20\) and \(c=40\) --> ratio of the amounts spent would be (20*150)/(40*50)=3/2.

Hope it's clear.
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Re: A company bought some desks at a price of $150 each and some  [#permalink]

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New post 02 Jun 2012, 00:45
Bunuel wrote:
The red part is not correct. The fact that the prices are in ratio 3 to 1, does not necessarily mean that the total amount spent would also be in the same ratio. For example consider \(d=20\) and \(c=40\) --> ratio of the amounts spent would be (20*150)/(40*50)=3/2.
Hope it's clear.


Thanks Bunuel for clarifying my doubt. Is there any specific case in which this generalization can be true? Or it is always incorrect to assume this?

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Re: A company bought some desks at a price of $150 each and some  [#permalink]

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