Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
GMAT Club Daily Prep
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jul 2710:00 AM PDT
-11:00 AM PDT
Are you struggling with the GMAT verbal section? Do tricky questions and lengthy passages overwhelm you? Don't worry—I've got you covered! In this video, I'll provide a detailed, actionable plan to help you significantly boost your verbal score.
Jul 2711:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
Jul 2508:00 AM EDT
-11:59 PM EDT
More and more TTP students are earning impressive scores on the GMAT. Now is the perfect time to join the many GMAT students who made the switch to TTP and surpassed their wildest expectations on test day.- Jul 28
10:00 AM PDT
-11:00 AM PDT
We will learn how to guess an answer choice better on the GMAT. If you are running out of time and want to guess on a few questions, these effective techniques will help you in making a smart guess. - Jul 28
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. - Jul 31
05:55 AM PDT
-12:30 PM PDT
MBA Application Walkthrough and Essay Review. You will have a chance to hear from experts covering the Top 15 MBA programs, covering details of the application and essays. 
Jul 3110:00 AM EDT
-11:59 PM PDT
Save 20% on Target Test Prep and Score in the 100th Percentile in GMAT Verbal! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
A spherical balloon originally had a radius of x centimeters. The ball
[#permalink]
01 Aug 2023, 03:00
01 Aug 2023, 03:00
32
Bookmarks
Expert Reply
Show timer
00:00
A
B
C
D
E
Difficulty:
45%
(medium)
Question Stats:
75% (02:33) correct
25%
(02:31)
wrong
based on 260
sessions
A spherical balloon originally had a radius of x centimeters. The balloon was partially deflated by letting out some air so that the volume of the balloon decreased by a%. If the balloon remained spherical while the air was being let out, which of the following expressions in x and a gives the radius, in centimeters, of the partially deflated balloon?
(Note: The volume of a sphere with radius r is \(\frac{4}{3}πr^3\).)
A. \(x(100 - a)^3\)
B. \(x(1 - \frac{a}{100})^3\)
C. \(x(\sqrt[3]{100 - a})\)
D. \(x(\sqrt[3]{1 - \frac{a}{100}})\)
E. \(x(1 - \sqrt[3]{\frac{a}{100}})\)
(Note: The volume of a sphere with radius r is \(\frac{4}{3}πr^3\).)
A. \(x(100 - a)^3\)
B. \(x(1 - \frac{a}{100})^3\)
C. \(x(\sqrt[3]{100 - a})\)
D. \(x(\sqrt[3]{1 - \frac{a}{100}})\)
E. \(x(1 - \sqrt[3]{\frac{a}{100}})\)
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3036
Given Kudos: 1646
A spherical balloon originally had a radius of x centimeters. The ball
[#permalink]
01 Aug 2023, 07:27
01 Aug 2023, 07:27
4
Kudos
2
Bookmarks
Expert Reply
Bunuel wrote:
A spherical balloon originally had a radius of x centimeters. The balloon was partially deflated by letting out some air so that the volume of the balloon decreased by a%. If the balloon remained spherical while the air was being let out, which of the following expressions in x and a gives the radius, in centimeters, of the partially deflated balloon?
(Note: The volume of a sphere with radius r is \(\frac{4}{3}πr^3\).)
A. \(x(100 - a)^3\)
B. \(x(1 - \frac{a}{100})^3\)
C. \(x(\sqrt[3]{100 - a})\)
D. \(x(\sqrt[3]{1 - \frac{a}{100}})\)
E. \(x(1 - \sqrt[3]{\frac{a}{100}})\)
(Note: The volume of a sphere with radius r is \(\frac{4}{3}πr^3\).)
A. \(x(100 - a)^3\)
B. \(x(1 - \frac{a}{100})^3\)
C. \(x(\sqrt[3]{100 - a})\)
D. \(x(\sqrt[3]{1 - \frac{a}{100}})\)
E. \(x(1 - \sqrt[3]{\frac{a}{100}})\)
The original volume of the balloon is:
(4/3)(pi)(x^3)
Since an a% decrease corresponds to a factor of (1 - a/100), the volume of partially deflated balloon is:
(4/3)(pi)(x^3)(1 - a/100)
If r is the radius of the partially deflated balloon, we have:
(4/3)(pi)(r^3) = (4/3)(pi)(x^3)(1 - a/100)
r^3 = (x^3)(1 - a/100)
r = (x)(root[3](1 -a/100))
Answer: D
General Discussion
Re: A spherical balloon originally had a radius of x centimeters. The ball
[#permalink]
14 Oct 2023, 13:42
14 Oct 2023, 13:42
Any suggestions on ways to do this by plugging in?
