Last visit was: 24 Apr 2025, 19:22 It is currently 24 Apr 2025, 19:22
Close
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
enigma123
Joined: 25 Jun 2011
Last visit: 16 Mar 2016
Posts: 393
Own Kudos:
Given Kudos: 217
Status:Finally Done. Admitted in Kellogg for 2015 intake
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
GMAT 1: 730 Q49 V45
Posts: 393
Kudos: 18,351
 [384]
40
Kudos
Add Kudos
343
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2025
Posts: 100,914
Own Kudos:
Given Kudos: 93,176
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 100,914
Kudos: 719,265
 [193]
71
Kudos
Add Kudos
121
Bookmarks
Bookmark this Post
avatar
independentm
Joined: 11 Apr 2012
Last visit: 26 Oct 2014
Posts: 6
Own Kudos:
31
 [30]
Given Kudos: 4
Posts: 6
Kudos: 31
 [30]
16
Kudos
Add Kudos
14
Bookmarks
Bookmark this Post
General Discussion
User avatar
LalaB
User avatar
Current Student
Joined: 23 Oct 2010
Last visit: 17 Jul 2016
Posts: 228
Own Kudos:
1,235
 [66]
Given Kudos: 73
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Posts: 228
Kudos: 1,235
 [66]
45
Kudos
Add Kudos
21
Bookmarks
Bookmark this Post
(40-10)*t=6

t=1/5 mins

(1/5)*60=12 sec
avatar
abid1986
Joined: 01 Jan 2013
Last visit: 09 Sep 2016
Posts: 38
Own Kudos:
135
 [16]
Given Kudos: 131
Location: India
Posts: 38
Kudos: 135
 [16]
10
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
enigma123
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


Work done by Faster gear Q is 6 more than slower gear P in same time

i.e W(q) = W(p) + 6
Rq X t = Rp X t + 6
40t=10t + 6
30t = 6
t =1/5 hrs
t = 12 mins
avatar
wfmd
Joined: 19 Aug 2013
Last visit: 26 Jul 2015
Posts: 15
Own Kudos:
19
 [8]
Location: Germany
Concentration: International Business, Technology
Schools: HKU '15 (A)
GMAT 1: 580 Q35 V35
GMAT 2: 690 Q44 V40
GPA: 3.85
WE:Information Technology (Consulting)
Schools: HKU '15 (A)
GMAT 2: 690 Q44 V40
Posts: 15
Kudos: 19
 [8]
6
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
My approach was the following (similar to what LalaB wrote):

Difference between gears Q and P is 30 revolutions per min (40-10).
To make 6 more rotations, the faster gear needs (6 rev / 30 rev/min = 1/5 min). Translate to seconds: 1/5 x 60 = 12.
avatar
Swaminathan1986
Joined: 13 Jan 2014
Last visit: 03 Aug 2018
Posts: 2
Own Kudos:
9
 [7]
Given Kudos: 1
Posts: 2
Kudos: 9
 [7]
4
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
enigma123
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

All the above answers are excellent and I would like to one little tweak that has helped me in quite a few number of Quant problems. This is applicable for people who love to find answers by plugging in the options given

As soon as you arrive at the 2 numbers "6 seconds and 1.5 seconds" (Time taken to complete one rotation) , look at the options given. The best options(9 out of 10 times) are the ones that are a multiple of the above two numbers. Hence you will possibly start with option A and then move to option B and voila.

NOTE: Use this method in scenarios such as this example wherein the number of options that fall under the "multiple umbrella"are quite low. If all the options are multiples it is better to switch on to one of the above strategies.
User avatar
oss198
Joined: 18 Jul 2013
Last visit: 01 Jan 2023
Posts: 69
Own Kudos:
397
 [14]
Given Kudos: 120
Location: Italy
GMAT 1: 600 Q42 V31
GMAT 2: 700 Q48 V38
GPA: 3.75
GMAT 2: 700 Q48 V38
Posts: 69
Kudos: 397
 [14]
10
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
----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
avatar
Amit0507
Joined: 26 May 2013
Last visit: 15 Aug 2016
Posts: 42
Own Kudos:
77
 [19]
Given Kudos: 243
Posts: 42
Kudos: 77
 [19]
18
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
enigma123
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

Another approach: P makes 10 R(evolutions) in 60 secs, so 1 R in 6 Sec. Similarly, as Q makes 40 R in 60 Sec or 4 R in 6 Sec. We can extrapolate the above details to state that P would make 2 R in 12 Sec and Q would make 8 R in 12 sec. Hence Q needs additional 12 Sec to overtake P by 6 Revolutions.
User avatar
kanigmat011
Joined: 27 Jul 2014
Last visit: 26 Dec 2019
Posts: 199
Own Kudos:
373
 [14]
Given Kudos: 15
Schools: ISB '15
GMAT 1: 660 Q49 V30
GPA: 3.76
Products:
Schools: ISB '15
GMAT 1: 660 Q49 V30
Posts: 199
Kudos: 373
 [14]
11
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
We can resolve this by as following

Gear P

Speed of gear P per second = 10revolutions/60 secs
=1/6 revolutions per second

Speed of gear Q per second = 40revolutions/60 secs
=4/6 revolutions per second

Distance travelled P Q
1sec 1/6 revolutions 4/6 revolutions
6 sec 1 revolution 4 revolution
12 sec 2 revolution 8 revolutions

Hence in 12 seconds Gear P completes 2 rev and Gear Q completes 8 rev
Difference =8-2= 6 revolutions
Therefore in 12 sec Gear Q revolves 6 times ahead than Gear P

Hope this makes it
Like my post Plz Send me Kudos :)
User avatar
mcelroytutoring
Joined: 10 Jul 2015
Last visit: 23 Apr 2025
Posts: 1,202
Own Kudos:
2,572
 [5]
Given Kudos: 282
Status:Expert GMAT, GRE, and LSAT Tutor / Coach
Affiliations: Harvard University, A.B. with honors in Government, 2002
Location: United States (CO)
Age: 45
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GMAT 4: 730 Q48 V42 (Online)
GRE 1: Q168 V169
GRE 2: Q170 V170
Expert
Expert reply
GMAT 4: 730 Q48 V42 (Online)
GRE 1: Q168 V169
GRE 2: Q170 V170
Posts: 1,202
Kudos: 2,572
 [5]
2
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Here's a visual that should help. Notice that I turned 6 into \(\frac{360}{60}\) to preserve the common denominator.
Attachments

Screen Shot 2016-03-23 at 5.49.06 PM.png
Screen Shot 2016-03-23 at 5.49.06 PM.png [ 61.57 KiB | Viewed 143554 times ]

User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 3,008
Own Kudos:
7,667
 [15]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 3,008
Kudos: 7,667
 [15]
8
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
enigma123
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
avatar
zanaik89
Joined: 19 Aug 2016
Last visit: 29 Nov 2019
Posts: 56
Own Kudos:
Given Kudos: 30
Posts: 56
Kudos: 7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
enigma123
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2025
Posts: 100,914
Own Kudos:
Given Kudos: 93,176
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 100,914
Kudos: 719,265
Kudos
Add Kudos
Bookmarks
Bookmark this Post
zanaik89
Bunuel
enigma123
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) = ?
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,793
Own Kudos:
12,340
 [5]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,793
Kudos: 12,340
 [5]
2
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
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
User avatar
AliciaSierra
Joined: 17 Mar 2014
Last visit: 14 Jun 2024
Posts: 748
Own Kudos:
Given Kudos: 1,350
Products:
Posts: 748
Kudos: 632
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel, can you share more such questions ?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2025
Posts: 100,914
Own Kudos:
Given Kudos: 93,176
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 100,914
Kudos: 719,265
 [17]
2
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
avatar
hsn81960
Joined: 16 May 2018
Last visit: 15 Aug 2019
Posts: 60
Own Kudos:
Given Kudos: 45
Location: Hungary
Posts: 60
Kudos: 7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
----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???
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,793
Own Kudos:
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,793
Kudos: 12,340
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
avatar
gmatapprentice
Joined: 14 Nov 2018
Last visit: 21 Apr 2021
Posts: 51
Own Kudos:
Given Kudos: 211
Location: United Arab Emirates
Concentration: Finance, Strategy
Schools: LBS '22 (I)
GMAT 1: 590 Q42 V30
GMAT 2: 670 Q46 V36
GPA: 2.6
Schools: LBS '22 (I)
GMAT 2: 670 Q46 V36
Posts: 51
Kudos: 14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
LalaB have you used the relative speed formula?
 1   2   
Moderators:
Math Expert
100914 posts
PS Forum Moderator
564 posts