• Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors

OG 130

This topic has 3 expert replies and 1 member reply

OG 130

Post
What is the volume of a certain rectangular solid?

1. Two adjacent faces of the solid have areas 15 and 24, respectively.
2. Each of wo opposite faces of the solid has area 40.


Explain reasoning

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
oquiella wrote:
What is the volume of a certain rectangular solid?

1. Two adjacent faces of the solid have areas 15 and 24, respectively.
2. Each of two opposite faces of the solid has area 40.
Target question: What is the volume of a certain rectangular solid?

Aside: A rectangular solid is a box

Statement 1: Two adjacent faces of the solid have areas 15 and 24, respectively.
There are several different rectangular solids that meet this condition. Here are two:
Case a: the dimensions are 1x15x24, in which case the volume is 360
Case b: the dimensions are 3x5x8, in which case the volume is 120
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Each of two opposite faces of the solid has area 40.
So, there are two opposite faces that each have area 40.
Definitely NOT SUFFICIENT

Statements 1 and 2 combined:
So, we know the area of each face (noted in blue on the diagram below).
Let's let x equal the length of one side.



Since the area of each face = (length)(width), we can express the other two dimensions in terms of x.


From here, we'll focus on the face that has area 40.
This face has dimensions (15/x) by (24/x)
Since the area is 40, we know that (15/x)(24/x) = 40
Expand: 360/(x^2) = 40
Simplify: 360 = 40x^2
Simplify: 9 = x^2
Solve: x = 3 or -3
Since the side lengths must be positive, we can be certain that x = 3

When we plug x=3 into the other two dimensions, we get 15/3 and 24/3
So, the 3 dimensions are 3, 5, and 8, which means the volume of the rectangular solid must be 120.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for our free Question of the Day emails
And check out all of our free resources



Last edited by Brent@GMATPrepNow on Mon Apr 16, 2018 12:50 pm; edited 2 times in total

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Master | Next Rank: 500 Posts Default Avatar
Joined
13 Nov 2015
Posted:
137 messages
Followed by:
2 members
Upvotes:
1
Post
Ok. I had a very different approach that made me think that statement 1 is sufficient.

Please tell me what i did wrong here.

I thought of 2 adjacent sides have areas of 15 and 24 then the following must be true:

LW = 15 or 24

WH = the other number

LW x WH = 15 x 24

the prime factorization of 15 and 24 yields to 3,3,2,2,2,5

Hence since LWxWh is LHW^2 then W^2 must be 3x3

Hence the width is equal to 3

so the volume of the triangle will be equal to 5x2x2x2x3, regardless of the allocation of those numbers to the lengths of the other sides.

for example if L is 10 and W is 4 or L is 20 and W is 2 the multiplication of those numbers will yield to the same volume. and hence I concluded that statement one is sufficient.

Why am I wrong????

PLs advise

Brent@GMATPrepNow wrote:
oquiella wrote:
What is the volume of a certain rectangular solid?

1. Two adjacent faces of the solid have areas 15 and 24, respectively.
2. Each of two opposite faces of the solid has area 40.
Target question: What is the volume of a certain rectangular solid?

Aside: A rectangular solid is a box

Statement 1: Two adjacent faces of the solid have areas 15 and 24, respectively.
There are several different rectangular solids that meet this condition. Here are two:
Case a: the dimensions are 1x15x24, in which case the volume is 360
Case b: the dimensions are 3x5x8, in which case the volume is 120
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Each of two opposite faces of the solid has area 40.
So, there are two opposite faces that each have area 40.
Definitely NOT SUFFICIENT

Statements 1 and 2 combined:
So, we know the area of each face (noted in blue on the diagram below).
Let's let x equal the length of one side.



Since the area of each face = (length)(width), we can express the other two dimensions in terms of x.


From here, we'll focus on the face that has area 40.
This face has dimensions (15/x) by (24/x)
Since the area is 40, we know that (15/x)(24/x) = 40
Expand: 360/(x^2) = 40
Simplify: 360 = 40x^2
Simplify: 9 = x^2
Solve: x = 3 or -3
Since the side lengths must be positive, we can be certain that x = 3

When we plug x=3 into the other two dimensions, we get 15/3 and 24/3
So, the 3 dimensions are 3, 5, and 8, which means the volume of the rectangular solid must be 120.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Hi amrabdelnaby,

This DS question asks us for the VOLUME of the rectangular solid, so we need to know the length, width and height of this shape. If those numbers can change, then the volume will almost certainly change.

1) Two adjacent faces of the solid have areas 15 and 24, respectively.

Fact 1 gives us the areas of two adjacent faces, but we do NOT know the exact dimensions...

IF....
the dimensions are 1x15 and 1x24, then the volume = (1)(15)(24) = 360
the dimensions are 5x3 and 3x8, then the volume = (5)(3)(8) = 120
Fact 1 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

GMAT Instructor Default Avatar
Joined
12 Sep 2012
Posted:
2637 messages
Followed by:
114 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post
Amrabdelnaby wrote:
Ok. I had a very different approach that made me think that statement 1 is sufficient.

Please tell me what i did wrong here.
I like the idea, but you can't assume that the sides are integers, especially not factors of 15 and 24. (The test WANTS you to assume this -- it would be nice if it were true -- but it doesn't have to be.)

Algebra could save us here: we have

WH = 15
HL = 24

So we could have H = 9, W = (15/9), and L = (24/9), or some other ghastly combination.

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

Top First Responders*

1 Jay@ManhattanReview 81 first replies
2 Brent@GMATPrepNow 71 first replies
3 fskilnik 55 first replies
4 GMATGuruNY 37 first replies
5 Rich.C@EMPOWERgma... 16 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik

GMAT Teacher

202 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

163 posts
3 image description Scott@TargetTestPrep

Target Test Prep

118 posts
4 image description Jay@ManhattanReview

Manhattan Review

94 posts
5 image description Max@Math Revolution

Math Revolution

94 posts
See More Top Beat The GMAT Experts