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# A company wants to buy computers and printers for a new branch office

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Senior Manager
Joined: 10 Mar 2013
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A company wants to buy computers and printers for a new branch office  [#permalink]

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17 Jan 2016, 02:37
12
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:11) correct 33% (02:31) wrong based on 303 sessions

A company wants to buy computers and printers for a new branch office, and the number of computers can be at most 3 times the number of printers. Computers cost $1,500 each, and printers cost$300 each. What is the greatest number of computers that the company can buy if it has a total of $9,100 to spend on computers and printers? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 Senior Manager Joined: 10 Mar 2013 Posts: 495 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) A company wants to buy computers and printers for a new branch office [#permalink] ### Show Tags Updated on: 17 Jan 2016, 13:54 1 BrainLab wrote: A company wants to buy computers and printers for a new branch office, and the number of computers can be at most 3 times the number of printers. Computers cost$1,500 each, and printers cost $300 each. What is the greatest number of computers that the company can buy if it has a total of$9,100 to spend on computers and printers?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

$$1500c+300p=9100$$ (max) -> $$15c+3p=91$$ -> $$c=\frac{91-3p}{15}$$
Max # of computers that one can buy is 6*15=90, BUT we have a restriction C ≤ 3P
If we buy 1 printer we can buy max. 5 computers - but the restriction is not satisfied, 2 printers -> 5 computers OK
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Originally posted by BrainLab on 17 Jan 2016, 02:41.
Last edited by BrainLab on 17 Jan 2016, 13:54, edited 2 times in total.
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Re: A company wants to buy computers and printers for a new branch office  [#permalink]

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17 Jan 2016, 07:59
3
BrainLab wrote:
A company wants to buy computers and printers for a new branch office, and the number of computers can be at most 3 times the number of printers. Computers cost $1,500 each, and printers cost$300 each. What is the greatest number of computers that the company can buy if it has a total of $9,100 to spend on computers and printers? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Tricky question in it that the total money of 9100$ is not the exact total required to buy the maximum number of computers at hand.

You are given c $$\leq$$ 3p ---> c/3 $$\leq$$ p ...(1)

Additionally, 1500c+300p=9100 ---> p = (91-15c)/3 and from 1 we get, (91-15c)/3 $$\geq$$ c/3

Thus we get, 16c $$\leq$$ 91 ---> c $$\leq$$ 5.XXX and as number of computers MUST be integers, the maximum value of 'c' can thus be = 5.

Hope this helps.
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A company wants to buy computers and printers for a new branch office  [#permalink]

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19 Jan 2016, 14:00
1
1
if C<= 3P, then C/3 <= P

1500C + 300P = 9100 can simplify to 15C + 3P = 91

The maximum C can equal is 3P so let's plug in C/3 for P in the above equation.

15C + (3)*(C/3) = 15C + C = 91 --> 16C = 91

So we need to figure out the max number of C that fits into 91. The answer is 5 (6 is too much as 16*6 = 96) and thus D.
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Re: A company wants to buy computers and printers for a new branch office  [#permalink]

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08 Aug 2018, 22:36
1
BrainLab wrote:
A company wants to buy computers and printers for a new branch office, and the number of computers can be at most 3 times the number of printers. Computers cost $1,500 each, and printers cost$300 each. What is the greatest number of computers that the company can buy if it has a total of $9,100 to spend on computers and printers? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Simple calculation is as below. Posted from my mobile device Attachments 15337929736138294124367117603922.jpg [ 1.91 MiB | Viewed 1903 times ] _________________ Everything is in flux, nothing stays still MGMAT1 :590 Q42 V30 (07/07/18) VERITAS :660 Q48 V33 (16/07/18) GMATPREP1 :690 Q46 V36 (22/07/18) GMATPREP2 :740 Q51 V39 (06/08/18) ECONOMIST :740 Q49 V44 (11/08/18) KAPLAN :690 Q49 V36 (17/08/18) PRINCETON :690 Q48 V38 (26/08/18) MGMAT2 :720 Q43 V45 (02/09/18) Manager Joined: 10 Jan 2013 Posts: 215 Location: India Concentration: General Management, Strategy GPA: 3.95 Re: A company wants to buy computers and printers for a new branch office [#permalink] ### Show Tags 08 Aug 2018, 22:44 1 BrainLab wrote: A company wants to buy computers and printers for a new branch office, and the number of computers can be at most 3 times the number of printers. Computers cost$1,500 each, and printers cost $300 each. What is the greatest number of computers that the company can buy if it has a total of$9,100 to spend on computers and printers?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

15c + 3p = 91

put the value of c as 6 but the condition is the c=3p (max)

so c =5 satisfies
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A company wants to buy computers and printers for a new branch office  [#permalink]

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17 Jan 2019, 08:13
Using single variable :

To get maximum number of computers -
Take the "atmost" ratio of computers : printers = $$3 : 1$$
Let number of computers = $$x$$ ------ then number of printers =$$x/3$$

$$1500x + 300 * \frac{x}{3}= 9100$$

$$15x + x = 91$$ -------- (just dividing each side by 100)

Now just plug in values of $$x$$ from AC and we see 5 works fine!
A company wants to buy computers and printers for a new branch office   [#permalink] 17 Jan 2019, 08:13
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