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Re: A company bought some desks at a price of $150 each and some chairs at [#permalink]
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
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Re: A company bought some desks at a price of $150 each and some chairs at [#permalink]
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 chairs at [#permalink]
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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 chairs at [#permalink]
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 chairs at [#permalink]
mokap25 wrote:
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

Kaps


let there be d desks and c chairs.

Start with statement 2. d<20, says nothing about c. Insufficient.


Statement 1. d150 + c50= 5000
3d + c = 100

(d,c) can be (10,70) as well as (30,10) so we can't say c>40.

Combine 1+2

we know that d<20, number of chairs can't be -ve so let's assume 19
19*3 + c= 100,
c= 100 - 57 = 43, so yes we can answer the question using statement 1 and 2 together.
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Re: A company bought some desks at a price of $150 each and some chairs at [#permalink]
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Re: A company bought some desks at a price of $150 each and some chairs at [#permalink]
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