GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 16 Jul 2020, 06:36

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

### Show Tags

29 May 2012, 21:30
9
00:00

Difficulty:

35% (medium)

Question Stats:

76% (01:52) correct 24% (01:40) wrong based on 214 sessions

### HideShow timer Statistics

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.

Kaps
SVP
Joined: 24 Jul 2011
Posts: 2113
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: NEW GMATPREP 2.1- OPTIMIZATION PROBLEM CAN SOME EXPERTS HELP  [#permalink]

### Show Tags

29 May 2012, 23:23
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. _________________ GyanOne [www.gyanone.com]| Premium MBA and MiM Admissions Consulting Awesome Work | Honest Advice | Outstanding Results Reach Out, Lets chat! Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services Math Expert Joined: 02 Sep 2009 Posts: 65384 Re: A company bought some desks at a price of$150 each and some  [#permalink]

### Show Tags

29 May 2012, 23:59
3
1
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.

Hope it's clear.
_________________
Intern
Joined: 10 Apr 2008
Posts: 24
Location: India
GMAT 1: 560 Q39 V28
WE: Consulting (Computer Software)
Re: A company bought some desks at a price of $150 each and some [#permalink] ### Show Tags 01 Jun 2012, 02:28 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?

AMeya
Intern
Joined: 30 Mar 2012
Posts: 29

### Show Tags

01 Jun 2012, 06:55
1
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. _________________ Intern Joined: 10 Apr 2008 Posts: 24 Location: India GMAT 1: 560 Q39 V28 WE: Consulting (Computer Software) Re: A company bought some desks at a price of$150 each and some  [#permalink]

### Show Tags

01 Jun 2012, 23:45
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?

Ameya
BSchool Moderator
Joined: 08 Dec 2013
Posts: 794
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)

### Show Tags

27 May 2020, 01:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________