GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 May 2019, 22:21 ### 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

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. ### Request Expert Reply # Two cars are racing along two concentric circular paths. What is the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55231
Two cars are racing along two concentric circular paths. What is the  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 63% (02:05) correct 37% (01:21) wrong based on 21 sessions

### HideShow timer Statistics

Two cars are racing along two concentric circular paths. What is the ratio of the speed of the car on the outer circle to that on the inner circle, if they were to complete a lap in the same amount of time?

(1) The difference in the area between the outer circle and the inner circle is 192π.
(2) The difference in radius between the outer circle and the inner circle is 8.

_________________
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2931
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Two cars are racing along two concentric circular paths. What is the  [#permalink]

### Show Tags

Bunuel wrote:
Two cars are racing along two concentric circular paths. What is the ratio of the speed of the car on the outer circle to that on the inner circle, if they were to complete a lap in the same amount of time?

(1) The difference in the area between the outer circle and the inner circle is 192π.
(2) The difference in radius between the outer circle and the inner circle is 8.

CONCEPT: Ratio of speeds = Ratio of distances when the time is constant

Question: What is the ratio of the speed of the car on the outer circle to that on the inner circle,

Statement 1: The difference in the area between the outer circle and the inner circle is 192π
i.e.$$π(R^2-r^2) = 192π$$
This doesn't give us the ratio fo distance hence
NOT SUFFICIENT

Statement 2: The difference in radius between the outer circle and the inner circle is 8
i.e. $$R-r =8$$
but different values of R and r are possible giving us different ratios of the distance covered by two cars hence
NOT SUFFICIENT

COmbining the two statements
$$π(R^2-r^2) = 192π$$
i.e. $$π*(R-r)*(R+r) = 192π$$ and also $$R-r =8$$
hence R and r can be calculated and ratio of distances may be calculated hence
SUFFICIENT

Answer: Option C
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern  B
Joined: 02 May 2018
Posts: 11
GMAT 1: 620 Q46 V29 Two cars are racing along two concentric circular paths. What is the  [#permalink]

### Show Tags

Bunuel wrote:
Two cars are racing along two concentric circular paths. What is the ratio of the speed of the car on the outer circle to that on the inner circle, if they were to complete a lap in the same amount of time?

(1) The difference in the area between the outer circle and the inner circle is 192π.
(2) The difference in radius between the outer circle and the inner circle is 8.

Speed = Distance/Time.
For the same time, the ratio of speed = ratio of distance = $$\frac{diameter of outercircle}{diameter of innercircle} = \frac{R}{r}$$
where $$R$$ is the radius of outer circle and $$r$$ is the radius of inner circle

a) Area of outer circle - Area of inner circle = $$192\pi$$
i.e $$\pi R^2$$ - $$\pi r^2$$ = $$192\pi$$.
Not sufficient

b) Radius of outer circle R - radius of inner circle r = 8
Not sufficient

Combining both
We have two equations, a quadratic equation and a linear equation and two unknowns. So we can jump straight to answer C

Wait..
Since it is a 600-level, I jumped straight to answer C.
However if it had been a 700-level problem, I would have gone one more step further, as the quadratic equation may have two solutions.
So the two equations are
$$\pi R^2$$ - $$\pi r^2$$ = $$192\pi$$
$$R$$ - $$r$$ = $$8$$

substituting second equation in the first
$$(r+8)^2$$ - $$r^2$$ = $$192$$
$$16r$$ + $$64$$ = $$192$$ and thus we can solve for r since $$r^2$$ cancels off.
However sometimes $$r^2$$ might not cancel and we may get two solutions for $$r$$ and in that case we might not be able to solve for unique solution for r.
Ironically, I find that the difficulty level of each question is making my approach to the problem different. I have to change it.
Anyway sometimes better to go one more step in solving equations, just to confirm...

So answer is C here Two cars are racing along two concentric circular paths. What is the   [#permalink] 15 Sep 2018, 02:11
Display posts from previous: Sort by

# Two cars are racing along two concentric circular paths. What is the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  