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# A company hired a printer to produce a total of x + 1

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Manager
Joined: 29 Nov 2011
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A company hired a printer to produce a total of x + 1 [#permalink]

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21 Feb 2012, 02:45
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Difficulty:

65% (hard)

Question Stats:

65% (03:27) correct 35% (02:50) wrong based on 289 sessions

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A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 2¢ envelopes and 5¢ envelopes. If the company requested 3 more 2¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?

A) 3x + 1

B) (7x - 2)/2

C) 11x + 31

D) (7x - 6)/2

E) (13x + 3)/2

Can anyone explain using picking numbers approach?
[Reveal] Spoiler: OA
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21 Feb 2012, 03:02
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Smita04 wrote:
A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 2¢ envelopes and 5¢ envelopes. If the company requested 3 more 2¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?

A) 3x + 1

B) (7x - 2)/2

C) 11x + 31

D) (7x - 6)/2

E) (13x + 3)/2

Can anyone explain using picking numbers approach?

Let the # of 5¢ envelopes be 2, then # of 2¢ envelopes will be 5, total=2+5=7 envelopes: x+1=7 --> x=6.
Cost: 5¢*2+2¢*5=20¢.

Now, plug x=6 in answer choices and see which one gives 20¢:

B. (7x - 2)/2=(7*6-2)/2=20¢. Correct.

Note that for plug-in method it might happen that for some particular numbers more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only. For example numbers 1 and 4 gives two "correct" choices A and B.

Hope it helps.
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Re: A company hired a printer to produce a total of x + 1 [#permalink]

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21 Feb 2012, 05:18
Thanks Bunuel, it definitely helped.
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Re: A company hired a printer to produce a total of x + 1 [#permalink]

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31 May 2013, 06:23
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
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Re: A company hired a printer to produce a total of x + 1 [#permalink]

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31 May 2013, 07:18
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Let the number of

2c envelopes = p
5c envelopes = q

Given

P = q + 3
P+q=x+1

=> 2q+3 = x+1

Q = x-2/2

Total cost = 2p + 5q substituting p = q+3 we get

= 7q +6 substituting for q

7x - 2/2
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Re: A company hired a printer to produce a total of x + 1 [#permalink]

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31 May 2013, 07:19
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Expert's post
Smita04 wrote:
A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 2¢ envelopes and 5¢ envelopes. If the company requested 3 more 2¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?

A) 3x + 1

B) (7x - 2)/2

C) 11x + 31

D) (7x - 6)/2

E) (13x + 3)/2

Can anyone explain using picking numbers approach?

Assume that no of 5 cents envelopes = 0. Thus, the no of 2 cents envelopes = 3. Total cost = 6 cents. Also, the total no of envelopes,x+1 = 3--> x=2. Only B gives 6 cents for x=2.
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Re: A company hired a printer to produce a total of x + 1 [#permalink]

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02 Jun 2013, 13:41
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Let x = 6, hence x +1 = 7

the company requested 3 more 2¢ envelopes than 5¢ envelopes

let y be the number of required 5¢ envelopes,

therefore (y+3) is the required number of 2¢ envelopes

y + y + 3 = total number of envelopes = x+ 1,therefore y + y + 3 = 7

2y = 4

y = 2, (y+3) = 5

cost of 2¢ envelopes = 5 * 2 = 10 cents

cost of 5¢ envelopes = 2 * 5 = 10 cents

Total Cost = 20 cents, plugging back into the answer choices

choice b : (7x - 2)/2 = (7*6 -2)/2 = 40/2 = 20 cents
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Re: A company hired a printer to produce a total of x + 1 [#permalink]

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10 Jan 2014, 10:36
Smita04 wrote:
A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 2¢ envelopes and 5¢ envelopes. If the company requested 3 more 2¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?

A) 3x + 1

B) (7x - 2)/2

C) 11x + 31

D) (7x - 6)/2

E) (13x + 3)/2

Can anyone explain using picking numbers approach?

Yeah smart numbers works well here.

X+1 = 7
X= 6

So 2c envelopes will be 5
and 5c envelopes will be 2

So total cost will be 20

Then that is our target

Plug x =6 in answer choices

Only B works

Hope it helps
Cheers!
J
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Re: A company hired a printer to produce a total of x + 1 [#permalink]

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11 Mar 2015, 07:31
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).

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A company hired a printer to produce a total of x + 1 [#permalink]

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03 Sep 2015, 11:21
let t=# two cent envelopes
let f=# five cent envelopes
total cost=2t+5f
1. t+f=x+1
2. t-f=3
adding 1 & 2 ➡ t=(x+4)/2
subtracting 2 from 1 ➡ f=(x-2)/2
substituting in 2t+5f, then 2(x+4/2)+5(x-2/2)=(7x-2)/2
A company hired a printer to produce a total of x + 1   [#permalink] 03 Sep 2015, 11:21
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