Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Danny is sitting on a rectangular box. The area of the front [#permalink]
06 Nov 2012, 17:03

1

This post received KUDOS

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

62% (03:36) correct
38% (02:38) wrong based on 165 sessions

Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 24, what is the area of the side face of the box?

You grossly underestimated the time this question took you. You actually solved it in 10 minutes and 33 seconds.

Correct.

Applying the relationship of the surface areas of the three sides, you can get the values of w and h in terms of l:

Side face = w x h

Top face = w x l = 1.5 x w x h which implies l = 1.5 h --> h = 2/3 l

Front face = l x h = 1.5/2 x w x h which implies l = 1.5/2 w --> w =4/3 l

Thus, the sides of the box: l, h and w, have the relationship of 1, 2/3 and 4/3 respectively such that the sides of the box are factors of 24. Expand the ratio times 3 to get rid of the fraction: l:h:w have the ratio of 3:2:4. It just so happens that 3×2×4 = 24, so these values also satisfy the question' requirements.

Hence, the area of side face is w x h = 4 x 2 = 8.

Wow, so I understand all the concepts here but I have to say, to be able to understand everything fully, and to do all the calculations required in this question would take a LOT of org and concentration skills not to make an easy error.

Anyone have any special insight on this on how to break it down in a more easier manner?

Re: Danny is sitting on a rectangular box. The area of the front [#permalink]
06 Nov 2012, 19:17

anon1 wrote:

Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 24, what is the area of the side face of the box?

You grossly underestimated the time this question took you. You actually solved it in 10 minutes and 33 seconds. Correct. Applying the relationship of the surface areas of the three sides, you can get the values of w and h in terms of l: Side face = w x h Top face = w x l = 1.5 x w x h which implies l = 1.5 h --> h = 2/3 l Front face = l x h = 1.5/2 x w x h which implies l = 1.5/2 w --> w =4/3 l Thus, the sides of the box: l, h and w, have the relationship of 1, 2/3 and 4/3 respectively such that the sides of the box are factors of 24. Expand the ratio times 3 to get rid of the fraction: l:h:w have the ratio of 3:2:4. It just so happens that 3×2×4 = 24, so these values also satisfy the question' requirements. Hence, the area of side face is w x h = 4 x 2 = 8. Wow, so I understand all the concepts here but I have to say, to be able to understand everything fully, and to do all the calculations required in this question would take a LOT of org and concentration skills not to make an easy error. Anyone have any special insight on this on how to break it down in a more easier manner?

Lets say, front face is made of l ,b top face is made of l,w and side face is made of b,w

question says, front face of the box is half the area of the top face, these faces will share one common side, lb =lw/2 => b=w/2

also that, area of the top face is 1.5 times the area of the side face, lw = 1.5 bw => l=3/2w

We want area of side face, A=bw We know Volume =lbw or V = A*l Thus all we need to know is l.

Re: Danny is sitting on a rectangular box. The area of the front [#permalink]
01 Mar 2014, 19:14

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: Danny is sitting on a rectangular box. The area of the front [#permalink]
03 Mar 2014, 21:45

Expert's post

anon1 wrote:

Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 24, what is the area of the side face of the box?

A. 3 B. 6 C. 8 D. 9 E. 12

If you want to minimize the use of too many variables, you can look at it another way:

Attachment:

Ques3.jpg [ 7.6 KiB | Viewed 1207 times ]

"The area of the front face of the box is half the area of the top face" - Front and top faces share the width so length must be half the depth. L = (1/2)D "the area of the top face is 1.5 times the area of the side face." - Top and side faces share the depth so width must be 1.5 times the length. W = (3/2)L = (3/4)D

Volume = 24 = D*(1/2)D*(3/4)D = (3/8)D D = 4

Side face area = D*L = 4*(1/2)*4 = 8 _________________

Great to know you are joining Kellogg. A lot was being talked about your last minute interview on Pagalguy (all good though). It was kinda surprise that you got the...

This is a long overdue post! A lot of Indian applicants, having scheduled interviews in March, reached out to me asking about my interview experience with Kellogg. I had a...

A critical phase of the MBA application, concurrent to researching your target schools, is “researching yourself” and building your profile. What are your unique traits? Where do you want to be...