New GMATprep 2.1-optimization type problem, experts help plz

Expert replies

kaps786: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Aug 13, 2011 8:34 am; Thanked: 2 times

by kaps786 » Tue May 29, 2012 9:26 pm

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?

The total price of the desk and chairs is 5,000
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.

OA is C

Thanks for your help

Kaps

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Source: Beat The GMAT — Data Sufficiency | Tue May 29, 2012 9:26 pm

sam2304: Legendary Member; Posts: 1239; Joined: Tue Apr 26, 2011 6:25 amFollowed by: 26 members; Thanked: 233 times; GMAT Score:680

by sam2304 » Tue May 29, 2012 9:38 pm

Given 150d + 50c

is c > 40 ?

1.150d + 50c = 5000
Only one eqn and we cannot solve

2.d < 20
Without the total cost and knowing # desks alone wouldn't help us find c.

comibining both. Use limits, we have an eqn and then d < 20

Assume d = 1.

150 +50c = 5000
50c = 4850
c = 97 so its greater than 40

Assume d = 19
150*19 + 50c = 5000
2850 + 50c =5000
50c = 2150
c = 43

So with both the statements either way we definitely have at least 40 chairs.

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mdavidm_531: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Mon Jun 07, 2010 3:12 am; Thanked: 10 times

by mdavidm_531 » Tue May 29, 2012 9:47 pm

kaps786 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?

The total price of the desk and chairs is 5,000
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.

OA is C

Thanks for your help

Kaps

Always start with the given

Desk price = $150
Chair price = $50

We let D = number of desks and C = number of chairs

The question is asking: is C > 40?

Statement (1) gives us: 150D + 50C = 5,000

C = 100 - 3D

Test values:
if....
D = 1 C = 97
D = 2 C = 94
D = 3 C = 91
D = 4 C = 88
and so on.. (we could see that we can't satisfy the equation)

Statement (2) gives us: D < 20

But this, in itself, doesn't help us = insufficient.

Statement (1) and Statement (2)

Here's how I do it

We know that d < 20, so I translate this as D = Lessthan20

Then I plug it in C = 100 - 3D
We have
C = 100 - 3(Lessthan20)
C = 100 - Lessthan60 (by intuition and a little bit of arithmetic)
C = Greaterthan 40 (by intuition and a little bit of arithmetic)

As such C > 40

We answered the question!

Sufficient! Answer is C!

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed May 30, 2012 3:38 am

kaps786 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?

The total price of the desk and chairs is 5,000
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.

OA is C

Thanks for your help

Kaps

Plug in the THRESHOLD.
In the question stem, the threshold is 40 CHAIRS.
The total cost of 40 chairs = 40*50 = 2000.

Statement 1: The total price of the desks and chairs is 5,000.
It is possible that 40 chairs are purchased (at a total cost of $2000) or that MORE CHAIRS are purchased.
INSUFFICIENT.

Statement 2: The company purchased fewer than 20 desks.
No way to determine the number of chairs purchased.
INSUFFICIENT.

Statements 1 and 2 combined:
The THRESHOLD in statement 2 is 20 desks.
The total cost of 20 desks = 20*150 = 3000.
If 20 desks are purchased at a cost of $3000, the remaining $2000 will be spent on exactly 40 chairs.
Since FEWER than 20 desks are purchased, the amount spent on the chairs must be GREATER than $2000, implying that MORE than 40 CHAIRS are purchased.
SUFFICIENT.

The correct answer is C.

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kaps786: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Sat Aug 13, 2011 8:34 am; Thanked: 2 times

by kaps786 » Wed May 30, 2012 8:17 am

Thanks all for your help and ideas; Mitch your approach is particularly elegant, thanks.

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GMAT Kolaveri: Master | Next Rank: 500 Posts; Posts: 287; Joined: Fri Mar 23, 2012 12:33 amFollowed by: 6 members; Location: Pune,India; Thanked: 60 times

by GMAT Kolaveri » Wed May 30, 2012 9:16 am

Question: Did the number of Chairs exceed 40?
What is required?
1. individual prizes of D and C(given)
2. Total amount spend (because we ll have a linear equation like nD + mC = ??/) NOT GIVEN
3. number of Desks or fraction of total amount spend on other entity(Desk) NOT GIVEN

Check both the S1 and S2 and start with the easier one. acc'ly use AD/BCE or BD/ACE
The total price of the desk and chairs is 5,000
The company bought fewer than 20 desks

Start with S2, the number of desk is less than 20. Could be 0 ,1,..or 19. Nothing is mentioned abt total amt. Hence Insufficient. BD ruled out.
Forget what we did in S2.
Start fresh with S1, only total amt spent is given, nothing regarding the number of D or C. Rule out A.

We are left with C and D,
Taking S1 and S2,Use extreme values.
nD + mC=5000
n < 20 Extreme value for n is 19. To make calc easier use n=20. With n=20 we get that m =40.
So with n <20 clearly m > 40 Hence C

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mcdesty: Master | Next Rank: 500 Posts; Posts: 116; Joined: Wed Mar 14, 2012 1:02 pmFollowed by: 11 members; Thanked: 20 times; GMAT Score:760

by mcdesty » Thu Aug 21, 2014 9:43 am

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Thu Aug 21, 2014 10:37 am

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

Given :
Price of Chair = $50, Let's say Number of Chairs Bought = C
Price of Desk = $150, Let's say Number of Desks Bought = D

Question : Is C > 40?

Statement 1) The total price of the desk and chairs is 5,000
i.e. 50C + 150D = 5000
i.e. C + 3D = 100
More than 1 Solutions are possible (e.g.C=25 & D=25 AND C=70 and D=10) therefore
INSUFFICIENT

Statement 2) The company bought fewer than 20 desks
No information about C therefore
INSUFFICIENT

Combining the two statements
C + 3D = 100 and D = 20
i.e. C = 40
SUFFICIENT

Answer: Option C

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