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

 It is currently 23 Aug 2019, 19:37 ### 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 # Circular gears P and Q start rotating at the same time at

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

### Hide Tags

Director  S
Joined: 12 Nov 2016
Posts: 708
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

Bunuel wrote:
enigma123 wrote:
Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Aany idea how to solve this?

Note that we are given revolutions per minute and asked about revolutions in seconds. So we should transform per minute to per second.

Gear P makes 10 revolutions per minute --> gear P makes 10/60 revolutions per second;
Gear Q makes 40 revolutions per minute --> gear Q makes 40/60 revolutions per second.

Let $$t$$ be the time in seconds needed for Q to make exactly 6 more revolutions than gear P --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Answer: D.

Hope it's clear.

It's definitely clear- I even reduced it to 10/60t +6=40/60t to 1/6t + 6 = 4/6t in order to make it more manageable- though if we can think quick enough it might help to use different variables like x since "t" under timed pressure can look like a plus sign and create stress- at least small things like those are what happened on my first GMAT and caused major blank outs.
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2819
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

enigma123 wrote:
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

As we can see, Gear Q makes 30 more revolutions per minute than Gear P does. So, we can set up the following proportion to solve for the number of seconds for Gear Q to make 6 more revolutions than Gear P does:

30 revolutions/1 minute = 6 revolutions/x seconds

We need the units of time to be the same in the denominator. Since 1 minute = 60 seconds, we can say:

30/60 = 6/x

Cross multiply and we have:

30x = 360

x = 12

Answer: D
_________________

# Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager  S
Joined: 03 Jan 2017
Posts: 139
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

let's translate into seconds:
P: 1/6 per second
Q: 2/3 per second
we can make the following equation: P*S=Q*S-6
6=s(q-p)
6=s*1/2
s=12
Answer is D
Intern  B
Joined: 14 May 2016
Posts: 20
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

Here is how I solved it:

Gear P

10 * 1 min/60 sec = 10/60 or 1/6

Gear Q

40 * 1 min/60 = 40/60 or 4/6

Now let's do ratios:

P Q
1/6 : 4/6

2/6 : 5/6

3/6 : 6/6

now lets cross multiply
P Q
3/6 * 4/6 = 12/6

hence answer is 12
Wharton Thread Master B
Joined: 30 May 2015
Posts: 36
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

very easy if you apply relative speed concept
Relative speed of P & Q is 30 RPM
so 30 Revolution in 60 sec
then 6 revolution will take 12 second Ans..
Intern  B
Joined: 24 Jan 2017
Posts: 48
Location: Brazil
Concentration: Strategy, Entrepreneurship
GPA: 3.5
WE: Consulting (Consulting)
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

Bunuel wrote:
enigma123 wrote:
Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Aany idea how to solve this?

Note that we are given revolutions per minute and asked about revolutions in seconds. So we should transform per minute to per second.

Gear P makes 10 revolutions per minute --> gear P makes 10/60 revolutions per second;
Gear Q makes 40 revolutions per minute --> gear Q makes 40/60 revolutions per second.

Let $$t$$ be the time in seconds needed for Q to make exactly 6 more revolutions than gear P --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Answer: D.

Hope it's clear.

Bunuel

I did this exercise using relative velocity:

P=> 10rev/60sec / Q=> 40rev/60sec / Vrel= 30rev/60sec or Vrel= 1rev/2sec Ω
So, 6 revolutions will take 12 seconds

Does it make sense? Or it was a lucky guess?!

TKS!!!
Manager  P
Joined: 13 Jun 2012
Posts: 202
Location: United States
WE: Supply Chain Management (Computer Hardware)
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

1
GuilhermeAzevedo wrote:
Bunuel wrote:
enigma123 wrote:
Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Aany idea how to solve this?

Note that we are given revolutions per minute and asked about revolutions in seconds. So we should transform per minute to per second.

Gear P makes 10 revolutions per minute --> gear P makes 10/60 revolutions per second;
Gear Q makes 40 revolutions per minute --> gear Q makes 40/60 revolutions per second.

Let $$t$$ be the time in seconds needed for Q to make exactly 6 more revolutions than gear P --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Answer: D.

Hope it's clear.

Bunuel

I did this exercise using relative velocity:

P=> 10rev/60sec / Q=> 40rev/60sec / Vrel= 30rev/60sec or Vrel= 1rev/2sec Ω
So, 6 revolutions will take 12 seconds

Does it make sense? Or it was a lucky guess?!

TKS!!!

Sorry not Bunnel, but I did it in the same way. Also, below is a method.

10T+6=40T ; 30T=6; T=1/5. now we have to convert it sec. so 1/5*60= 12
Manager  B
Joined: 19 Aug 2016
Posts: 80
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

Bunuel wrote:
enigma123 wrote:
Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Aany idea how to solve this?

Note that we are given revolutions per minute and asked about revolutions in seconds. So we should transform per minute to per second.

Gear P makes 10 revolutions per minute --> gear P makes 10/60 revolutions per second;
Gear Q makes 40 revolutions per minute --> gear Q makes 40/60 revolutions per second.

Let $$t$$ be the time in seconds needed for Q to make exactly 6 more revolutions than gear P --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Answer: D.

Hope it's clear.

Hi Bunuel,

How did u arrive at (10/60)t?

when speed is already 10/60

then time is t

are we calculating the distance here? Could u pls explain the logic to me?

Thanks in advance
Math Expert V
Joined: 02 Sep 2009
Posts: 57281
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

zanaik89 wrote:
Bunuel wrote:
enigma123 wrote:
Circular gears P & Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

A. 6
B. 8
C. 10
D. 12
E. 15

Aany idea how to solve this?

Note that we are given revolutions per minute and asked about revolutions in seconds. So we should transform per minute to per second.

Gear P makes 10 revolutions per minute --> gear P makes 10/60 revolutions per second;
Gear Q makes 40 revolutions per minute --> gear Q makes 40/60 revolutions per second.

Let $$t$$ be the time in seconds needed for Q to make exactly 6 more revolutions than gear P --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Answer: D.

Hope it's clear.

Hi Bunuel,

How did u arrive at (10/60)t?

when speed is already 10/60

then time is t

are we calculating the distance here? Could u pls explain the logic to me?

Thanks in advance

10/60 is the number of revolutions per second and t is the time in seconds. What would you get when you multiply those two? (revolutions per second)(time in seconds) = ?
_________________
Intern  Joined: 01 Dec 2017
Posts: 2
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

I thought about this problem in another way and wonder if this is also possible:
The rates of the two gears have a ratio of 4:1.
The question asks for +6 seconds.
My thought was, that the only number of the answers which has factors 4, 6 and 1 is 12. The solving process took me therefore only about 10 seconds. BUT I wonder if this is a possible approach or if this is just an example of luck?
Thank you for your answers!
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14856
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

1
Hi All,

Once you convert each rate into revolutions/second, TESTing THE ANSWERS is a remarkably easy way to get to the correct answer. Algebraically, you can treat it as a "combined rate" question though:

Distance = (Rate) x (Time)

6 revolutions = (difference in rates) x (Time)

6 revolutions = (30 revolutions/min) x (Time)

6/30 = Time in minutes

1/5 minute = Time

Since the question asks for an answer in SECONDS, we have to convert....

1/5 minute = 12 seconds

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin Follow
Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Manager  G Joined: 03 Oct 2012 Posts: 156 Location: India Concentration: Entrepreneurship, Strategy WE: Brand Management (Pharmaceuticals and Biotech) Re: Circular gears P and Q start rotating at the same time at [#permalink] ### Show Tags Well, would like to understand if my approach is correct: Gear P= 10/60 r/s = 1/6 r/s; Gear Q = 40/60 r/s = 2/3 r/s difference between faster & slower gears = 2/3-1/6 = 1/2 r/s = .5 r/s Now if gear Q gains .5 r in a second, it will require 2 seconds to gain 1 rev. Therefore, 2 seconds/rev x 6 revs = 12 seconds. Manager  B Joined: 14 Feb 2016 Posts: 71 Re: Circular gears P and Q start rotating at the same time at [#permalink] ### Show Tags Review: See this is as a classical relative rates problem – applying the formula RT = D. - In order to bridge the distance between the two gears, we take the rate of the faster gear and subtract that with the slower gear. Rp: 10/60 = 1/6. Rq = 10/60 = 1/4. - The question asks us – when will Q have made exactly 6 more revolutions than gear P? Rq – Rp = 3/6 = 1/2 . 1/2 is the rate at which Q makes more revolutions then P. So when will gear Q have made exactly 6 more revolutions than gear P? - 1/2 * T = 6 - T = 6*2 = 12. 12 seconds. Remember to convert minutes into seconds prior to playing with the formulas; as they ask for how many seconds after the gears start rotating…. _________________ Please provide kudos if you liked my post! I would really like to use the PDF file!! Senior Manager  P Joined: 17 Mar 2014 Posts: 437 Re: Circular gears P and Q start rotating at the same time at [#permalink] ### Show Tags Bunuel, can you share more such questions ? Math Expert V Joined: 02 Sep 2009 Posts: 57281 Re: Circular gears P and Q start rotating at the same time at [#permalink] ### Show Tags Senior Manager  P Joined: 09 Jun 2014 Posts: 343 Location: India Concentration: General Management, Operations Re: Circular gears P and Q start rotating at the same time at [#permalink] ### Show Tags Its relative speed concept here.. Note we can imagine distance in terms of revolutions here and its better to convert rev/min to rev/sec since answer is in seconds unit. Now, P speed= 10rev/min= 10/60 rev/sec=1/6 rev/sec Q speed = 40 rev/min = 40/60 = 2/3 rev/sec Now we need to make up for 6 revolutions an relative speed is 2/3-1/6=1/2 rev/sec There time taken to cover 6 rev = 6 /(1/2) = 12 seconds Press Kudos if it helps!! Manager  B Joined: 16 May 2018 Posts: 85 Location: Hungary Schools: Queen's MBA'20 Re: Circular gears P and Q start rotating at the same time at [#permalink] ### Show Tags ----RATE-----time--------distance P:---10 -----x/10------------ x Q:---40------(x+6)/40-------x+6 The time should be equal, so we solve x/10 = (x+6)/40 x=2 so time = 2/10 min = 12 sec Can anyone explain me how we get from x=2 ----> to 12 sec??? EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14856 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Circular gears P and Q start rotating at the same time at [#permalink] ### Show Tags Hi hsn81960, You did not label the "units" in your table, but based on the work that you presented, I think that you know that time is in MINUTES. You solved for X and got X=2... when you plug that back in for X you get: 2/10 = 1/5 of a minute for Gear P 8/40 = 1/5 of a minute for Gear Q Thus, it clearly takes 1/5 of a 1 minute for the revolutions to match what the question asked for. Since 1 minute = 60 seconds, then (1/5)(60) = 12 seconds GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Intern  B
Joined: 26 Sep 2018
Posts: 2
Re: Circular gears P and Q start rotating at the same time at  [#permalink]

### Show Tags

This is by far the easiest and fastest way to answer the question.

For P:

60 sec - 10 rev
1 sec - 1/6 rev

For Q:

60 sec - 40 rev
1 sec - 2/3 rev

Now, Q is revolving faster than P. So we can find the difference in revs as follows:

Difference in revs = Q-P
= 2/3 - 1/6
=(4-1)/6
=1/2 revs

so every second, the Q is making 1/2 rev more than P.

So Q would have made exactly 6 more revolutions than gear P in 6/(1/2)=12 secs Re: Circular gears P and Q start rotating at the same time at   [#permalink] 07 Aug 2019, 11:17

Go to page   Previous    1   2   [ 39 posts ]

Display posts from previous: Sort by

# Circular gears P and Q start rotating at the same time at

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  