BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

A cube has a volume of 72. If it is divided into 8 equal cub

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 426
Joined: Tue Aug 22, 2017 8:48 pmFollowed by: 1 member
by BTGmoderatorAT » Wed Dec 06, 2017 6:05 am
A cube has a volume of 72. If it is divided into 8 equal cubes, the ratio of an edge of a smaller cube to an edge of the original cube is

(A) 1 : 2
(B) 1: 3
(C) 1 : 3√2
(D) 2 : 9
(E) 1 : 9

I'm confused how to set up the formulas here. Can any experts help?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 100
Joined: Wed Nov 29, 2017 4:38 pm
Thanked: 14 times

by GMATWisdom » Wed Dec 06, 2017 8:01 am
ardz24 wrote:A cube has a volume of 72. If it is divided into 8 equal cubes, the ratio of an edge of a smaller cube to an edge of the original cube is

(A) 1 : 2
(B) 1: 3
(C) 1 : 3√2
(D) 2 : 9
(E) 1 : 9

I'm confused how to set up the formulas here. Can any experts help?
If the size of the edge of original cube is = a, its volume would be = a^3
And if the size of the edge of new cube is =b, its volume would be = b^3
Then ratio of volume of the new cube to the volume of original cube would be b^3 : a^3
In the present case a^3=72 and b^3= 72/8 = 9
Therefore b^3 : a^3 = 9 : 72
Or b^3 : a^3 = 1 : 8
Taking cube root of both the sides we get
b : a = 1 : 2
hence A is the correct answer
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
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 » Wed Dec 06, 2017 9:18 am
ardz24 wrote:A cube has a volume of 72. If it is divided into 8 equal cubes, the ratio of an edge of a smaller cube to an edge of the original cube is

(A) 1 : 2
(B) 1: 3
(C) 1 : 3√2
(D) 2 : 9
(E) 1 : 9
Great question!
The great thing about it is that the volume of the original cube is irrelevant.
It all comes down to what happens when we divide ANY cube into 8 equal cubes.
Here's what I mean.

Take a cube and divide it into 8 equal cubes...
Image

If we let x = the length of one edge of the ORIGINAL cube....
Image

....then x/2 = the length of one edge of the SMALLER cube....
Image

What is the ratio of an edge of a smaller cube to an edge of the original cube?
Get get: x/2 : x
Divide both sides by x to get the EQUIVALENT ratio: 1/2 : 1
Multiply both sides by 2 to get the EQUIVALENT ratio: 1 : 2

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members
Thanked: 180 times

by EconomistGMATTutor » Wed Dec 06, 2017 9:29 am
A cube has a volume of 72. If it is divided into 8 equal cubes, the ratio of an edge of a smaller cube to an edge of the original cube is

(A) 1 : 2
(B) 1: 3
(C) 1 : 3√2
(D) 2 : 9
(E) 1 : 9

I'm confused how to set up the formulas here. Can any experts help?
Hi ardz24,
Let's take a look at your question.

Volume of original cube = 72
Original cube is divided into 8 equal cubes, therefore, volume of each of the new cube will be:
$$=\frac{72}{8}=9$$

Let, edge length of original cube be 'x' and edge length of each of the new cubes is 'y', then,
$$x^3=72$$
$$y^3=9$$

Volume of new cube : Volume of Original cube
$$y^3\ :\ \ x^3 = 9\ :\ 72$$
$$y^3\ :\ \ x^3 =1\ :\ 8$$

But we are asked to find the ratio of an edge of a smaller cube to an edge of the original cube, i.e., x : y
$$y^3\ :\ \ x^3 =1\ :\ 8$$
$$y^3\ :\ \ x^3 =1^3\ :\ 2^3$$
$$y\ :\ \ x =1\ :\ 2$$

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1