A case contains c cartons.

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boomgoesthegmat: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Mon Apr 25, 2016 2:22 pmFollowed by: 1 member; Thanked: 1 times

by boomgoesthegmat » Mon Apr 25, 2016 2:34 pm

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

Answer: C

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Source: Beat The GMAT — Problem Solving | Mon Apr 25, 2016 2:34 pm

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by [email protected] » Mon Apr 25, 2016 3:55 pm

Hi boomgoesthegmat,

This question can be solved algebraically or by TESTing VALUES.

Let's TEST...
C = 2
B = 3

So each case contains 2 cartons and each carton contains 3 boxes. We're told that each box contains 100 paper clips, so that's a total of...

2(3)(100) = 600 paperclips in 1 case.

We're asked for the number of paperclips in 2 CASES though... so we're looking for an answer that equals 2(600) = 1200, when C=2 and B=3. There's only one answer that matches...

Final Answer: C

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Rich

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OptimusPrep: Master | Next Rank: 500 Posts; Posts: 410; Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members; Location: Worldwide; Thanked: 120 times; GMAT Score:770

by OptimusPrep » Mon Apr 25, 2016 8:21 pm

boomgoesthegmat 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

Answer: C

This question can be solved both by testing values and by algebra. I personally prefer algebra as it saves you sometime in such questions.

1 case = c cartons, 1 carton = b boxes, 1 box = 100 clips.
Number of clips in one box = c*b*100
Number of clips in 2 boxes = 2*c*b*100 = 200bc

Correct Option: C

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Apr 26, 2016 9:22 am

Rich and Ankur 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 videos:
- Variables in the Answer Choices - https://www.gmatprepnow.com/module/gmat- ... /video/933
- Tips for the Algebraic Approach - https://www.gmatprepnow.com/module/gmat- ... /video/934
- Tips for the Input-Output Approach - https://www.gmatprepnow.com/module/gmat- ... /video/935

Here are some more questions to practice with:
- https://www.beatthegmat.com/what-mistake ... 76293.html
- https://www.beatthegmat.com/car-dealer-s ... 74136.html
- https://www.beatthegmat.com/ps-rate-times-t276107.html
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- https://www.beatthegmat.com/a-better-exp ... 79396.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Wed Apr 27, 2016 2:34 pm

One last kinda mindless way of solving it:

We know that the number of clips must be greater than the number of boxes, since there's more than one paper clip in each box. That means that

# of paper clips > 2 * c * b

So we should have either A or C.

We remember that there are 100 paper clips PER box, so we should also have more than 100bc, as that represents in the number in one box.

From there it must be C, and we're set!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Mar 15, 2018 9:23 am

boomgoesthegmat 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

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.

Answer: C

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