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A case contains c cartons. Each carton contains b boxes, and

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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

A case contains c cartons. Each carton contains b boxes, and each box contains 100 paper clips. How many paper clips are contained in 2 cases?

(A) 100bc
(B) 100b/c
(C) 200bc
(D) 200b/c
(E) 200/bc

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SOLUTION

A case contains c cartons. Each carton contains b boxes, and each box contains 100 paper clips. How many paper clips are contained in 2 cases?

(A) 100bc
(B) 100b/c
(C) 200bc
(D) 200b/c
(E) 200/bc

Each case contains \(100bc\) paper clips, hence 2 cases contain \(200bc\) paper clips.

Answer: C.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A case contains c cartons. Each carton contains b boxes, and [#permalink]

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picking numbers

c = 5
b = 2

200 paperclips per carton
200 * 5 = 1000 per case

A. 1000
B. 200/5 = 40
C. 2000
D. 400/5 = 80
E. 20

[Reveal] Spoiler:
A.
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Re: A case contains c cartons. Each carton contains b boxes, and [#permalink]

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New post 24 Jul 2012, 08:15
To complete your answer, there are 2 cases so answer (C) is correct.
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Re: A case contains c cartons. Each carton contains b boxes, and [#permalink]

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New post 24 Jul 2012, 16:42
arthuro69 wrote:
To complete your answer, there are 2 cases so answer (C) is correct.


Ah yes. Disappointing on my part :(
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Re: A case contains c cartons. Each carton contains b boxes, and [#permalink]

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New post 09 Sep 2014, 19:43
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Case >> Carton >> Box >> Clips

Just multiplication required

Its 2 * (100 * b * c) = 200bc

Answer = C
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Re: A case contains c cartons. Each carton contains b boxes, and [#permalink]

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Bunuel wrote:
A case contains c cartons. Each carton contains b boxes, and each box contains 100 paper clips. How many paper clips are contained in 2 cases?

(A) 100bc
(B) 100b/c
(C) 200bc
(D) 200b/c
(E) 200/bc


Bunuel has already demonstrated an algebraic approach, so let's try solving it by picking some numbers (aka using the INPUT-OUTPUT approach).

Let b = 3 and c = 5
So, a case contains 5 cartons. Each carton contains 3 boxes, and each box contains 100 paper clips.
So, the number of paper clips in 1 case = (100)(5)(3) = 1500

How many paper clips are contained in 2 cases?
The number of paper clips in 2 cases = 3000

So, we're looking for the answer choice so that when we INPUT b = 3 and c = 5, we get an OUTPUT of 3000

Now check the answer choices:
(A) 100(3)(5) = 1500 ELIMINATE
(B) 100(3)/(5) = 60 ELIMINATE
(C) 200(3)(5) = 3000 KEEP!!
(D) 200(3)/(5) = 120 ELIMINATE
(E) 200/(3)(5) = 200/15 ELIMINATE

Answer: C

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As you can see, Bunuel and I have demonstrated the two methods (Algebraic and Input-Output) for solving a question type I call Variables in the Answer Choices.
If you'd like more information on these approaches, we have some free videos:

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Re: A case contains c cartons. Each carton contains b boxes, and [#permalink]

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Attached is a visual that should help.
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Screen Shot 2016-04-11 at 5.06.44 PM.png
Screen Shot 2016-04-11 at 5.06.44 PM.png [ 71.7 KiB | Viewed 12854 times ]


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A case contains c cartons. Each carton contains b boxes, and [#permalink]

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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

A case contains c cartons. Each carton contains b boxes, and each box contains 100 paper clips. How many paper clips are contained in 2 cases?

(A) 100bc
(B) 100b/c
(C) 200bc
(D) 200b/c
(E) 200/bc

Thank you![/textarea]


Solution:

We are given that a case contains c cartons. Each carton contains b boxes, and each box contains 100 paper clips. Thus we can say the following:

c x b x 100 = 100bc paper clips per case. Thus, 2 cases would contain 2 x 100bc = 200bc paper clips.

The answer is C.
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Re: A case contains c cartons. Each carton contains b boxes, and [#permalink]

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New post 02 Mar 2017, 21:06
I think you can draw this out (really helped me)

1 case --> 2 cartons --> 1 carton = 3 boxes --> 1 box = 100 pc
>> From here, there are 300 pc in 3 boxes (AKA 1 carton). Since you have 2 cartons here, in 1 case, you have 600 pc.
>> You want 2 cases, so you have 1,200 pc.

Plug in A/C w/ variables you defined above:
c=2 (cartons)
b=3 (boxes)


When you plug in, should give you: 1,200.

C) 200bc --> 200(3)(2) --> 200(6) --> 1,200
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Re: A case contains c cartons. Each carton contains b boxes, and [#permalink]

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Re: A case contains c cartons. Each carton contains b boxes, and   [#permalink] 05 Apr 2018, 07:29
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