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

Question

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

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

Bunuel · Accepted Answer

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

Show Spoiler

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

Show Answer

Official Answer

C

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GyanOne · Answer

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.

Ameya85 · Answer

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

slay3r · Answer

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

Bunuel · Answer

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.

Hope it's clear.

Ameya85 · Answer

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?

Ameya

LeoN88 · Answer

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.

DanTheGMATMan · Answer

40 chairs is 2000 bucks. 1 and 2 alone are clearly insufficient. Combined they've gotta spend more than 2 grand on chairs:

https://www.youtube.com/watch?v=4JgaAwEDp-k

Usernamevisible · Answer

The question is not asking to find the exact value of the number of chairs 
>> that's what I solved and got wrong

The question is asking whether the number of chairs is > 40 
Be careful

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

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

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