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

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Senior Manager
Joined: 11 May 2004
Posts: 430
Location: New York
Circular Gears P and Q start rotating at the same time at  [#permalink]

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07 Nov 2005, 17:49
1
10
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:06) correct 16% (01:16) wrong based on 272 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: circular-gears-p-and-q-start-rotating-at-the-same-time-at-129375.html

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Director
Joined: 21 Aug 2005
Posts: 751

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07 Nov 2005, 17:53
1
1
D) 12
P = 1/6 rev per sec
Q = 2/3 rev per sec
Let 't' be the time that we need to find out -
(1/6)x + 6 = (2/3)x => x=12
Intern
Joined: 15 Sep 2005
Posts: 9

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08 Nov 2005, 06:11
1
desiguy wrote:
Seems like a simple question, but I think I may be missing something...

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?

6
8
10
12
15

30 revs lead in 60 sec

6 rev lead in 60/30 * 6 = 12
Current Student
Joined: 28 Dec 2004
Posts: 3234
Location: New York City
Schools: Wharton'11 HBS'12

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08 Nov 2005, 07:27
2
I get 12 too...

bascially how GSR did it....

man...I have been partying 4 days straight...my brain is fried...and my boss is wondering where I am...guys...dont prolong your gmat...otherwise you get in to a state...i am in.... feel horrible now...so need to focus on gmat...focus on gmat...
SVP
Joined: 24 Sep 2005
Posts: 1784

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03 Apr 2006, 03:31
1
getzgetzu 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 the gear Q have made exactly 6 more revolutions than gear P?

6
8
10
12
15

Let x be the number of seconds which makes Q have 6 more revolutions than P.
In one second: P makes 1/6 revolution , Q makes 2/3 revolution
After x seconds : P makes x/6 revolutions, Q makes (2x)/3 revolutions
---> (2x)/3= x/6 + 6 --> x= (1/2)x = 6 --> x=12

D it is.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4836
Location: Singapore

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03 Apr 2006, 03:41
Assuming n minutes has passed when Q makes 6 revs more than P, then

10n + 6 = 40n
30n = 6
n = 1/5 minute = 12 seconds
Senior Manager
Joined: 03 May 2007
Posts: 262

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18 May 2007, 10:15
Rate for P=10r/m Q=40r/m convert it to r/seconds
P=1/6 r/m, Q=4/6 r/m

we get (4/6-1/6)*t=6 => 3t/6=6 t=12

VP
Joined: 08 Jun 2005
Posts: 1135

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18 May 2007, 10:22
1
1
Sergey_is_cool wrote:
Rate for P=10r/m Q=40r/m convert it to r/seconds
P=1/6 r/m, Q=4/6 r/m

we get (4/6-1/6)*t=6 => 3t/6=6 t=12

Sergey is right !

P = 10 revolutions in 60 seconds = 1/6 revolutions per second.

Q = 40 revolutions in 60 seconds = 2/3 revolutions per second.

after 12 seconds

P = 1/6*12 = 2 revolutions.

Q = 2/3*12 = 8 revolutions.

Intern
Joined: 15 Jan 2007
Posts: 38

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18 May 2007, 14:04
1
yes, look at it as Rate * time = distance.
so difference in distance is 6.
==> 4/6 * t - 1/6 * t = 6.

remember, t is same for both.
Intern
Joined: 02 Jun 2007
Posts: 27

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11 Jun 2007, 13:24
P makes 1/6 revs per sec
Q makes 4/6 revs per sec

t*(4/6) - t*(1/6) = 6
4t - t = 36
t = 12 seconds

Ans: 12
Senior Manager
Joined: 06 Mar 2006
Posts: 457

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16 Jul 2007, 13:09
2
Let's assume after x minutes Q has made exactly 6 more revolution than P.

since Q's speed is 40 revolution per minute and P's speed is 10 revolution per minute, the equation to solve will be 40x-10x=6
you can calculate from here that x=1/5 minutes.
However, the question asks for seconds. you need to convert 1/5 minutes to (1/5)*60 or 12 seconds. Therefore, D is the answer.
Manager
Joined: 07 Feb 2007
Posts: 54

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16 Jul 2007, 18:28
Q will be 30 revolutions (40 -10) ahead of P in 60 seconds.

Q will be 6 revolutions ahead of P in 60/30*6 secs = 12 (D).
Director
Joined: 08 Jun 2007
Posts: 550
Re: Gmat prep circular gears  [#permalink]

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16 Jul 2007, 19:59
n seconds (30/60)n ahead which is 6..which gives n =12
Senior Manager
Joined: 18 Aug 2009
Posts: 277
Re: How many seconds after the gears start rotating?  [#permalink]

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26 Apr 2010, 19:01
1
zz0vlb wrote:
Circular gears P and Q start rotating at the same time at constant speeds.Gear P makes 10 revolutions per min 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

Source: GMAT Prep

Q = 4P
P + 6 = Q = 4P
P = 2

So Q will complete 8 revolutions when P will complete 2. That is after 2/10*60 = 12 sec.
D
Current Student
Joined: 15 Dec 2009
Posts: 280
Schools: Duke

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08 Aug 2010, 18:32
2
If you don't immediately know the formula this is very good question to solve strategically by process of elimination, choose either answer B or D to begin with and see if you need a higher or lower timeframe. I immediately started with D) as it provided for good divisibilty of the numbers (btw. that by itself is a strong hint for the right answer for these kind of questions). So 12/60 is = 1/5. Now divide 40 revolution by 5 and the answer is 8 and divide 10 revolution by 5 and the answer is 2, the difference is 6, thus D) is the right answer.

Yes, the fact that the first POE was correct was somewhat lucky, but if it had been wrong you would have immediately eliminated D and either E or ABC. So either way you would have significantly narrowed down the answer. Worst case you would then also solve case B) and by then you would have for sure known what the answer was.

Just keep in mind, do not go through all the answer choices in order, if the answers are sorted (!), always to B) and/or D) as you will get more information quicker!!!!
_________________
Senior Manager
Status: GMAT Time...!!!
Joined: 03 Apr 2010
Posts: 272
Schools: Chicago,Tuck,Oxford,cambridge

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09 Aug 2010, 10:21
HI Yalephd, we have a seperate quant and verbal section for such questions.we request u to post such quant questions in PS/DS section from next time..

the answer D is correct as per thomas explaination..!!!

thanx
Intern
Joined: 03 Aug 2010
Posts: 26
Schools: Sloan '14 (M)
GRE 1: Q168 V169
WE: Engineering (Energy and Utilities)

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09 Aug 2010, 11:58
We are trying to find a specific time quantity. For this problem we can write the following equation for each gear

(Rate of L in rev/min) * (# of minutes) = total number of revolutions for L
(Rate of R in rev/min) * (# of minutes) = total number of revolutions for R

We are trying to solve for the number of minutes when

number of revolutions for L + 6 = number of revolutions for R

By substituting the first two formulas into the above equation we have:

(Rate of L in rev/min) * (# of minutes) + 6 = (Rate of R in rev/min) * (# of minutes)

10 * m + 6 = 40 * m
6 = 30 * m
6/30 = m

Remember that m has units of minutes, so we need to convert 6/30 minutes into seconds.

6/30 minutes * (60 seconds/min) = 12 seconds
Intern
Joined: 01 Jul 2010
Posts: 42
Schools: LBS, Harvard, Booth, Stanford, ISB, NTU
WE 1: S/W Engineer

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13 Aug 2010, 02:00
I cannot figure out how to go about this problem. Probably, because my brain is burned out due to an over-dosage of problems, or because, it is just refusing to think...
Thanks,
Janani
Attachment:

Prep1.jpg [ 86.7 KiB | Viewed 12243 times ]
Math Expert
Joined: 02 Sep 2009
Posts: 51121

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13 Aug 2010, 02:12
1
1
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?

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 --> $$\frac{10}{60}t+6=\frac{40}{60}t$$ --> $$t=12$$.

Hope it's clear.
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Manager
Joined: 18 Feb 2010
Posts: 152
Schools: ISB

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13 Aug 2010, 02:17
jananijayakumar wrote:
I cannot figure out how to go about this problem. Probably, because my brain is burned out due to an over-dosage of problems, or because, it is just refusing to think...
Thanks,
Janani
Attachment:
Prep1.jpg

Gear P = 10 revs/min

Gear q = 40 revs/min

A = 6 seconds = 1/10 of a minute so revs are 1 and 4 no

A = 8 seconds = 60/8 leave it for a while…..

A = 10 seconds = 1/6 of a minute so revs are 10/6 and 40/6 no

A = 12 seconds = 1/5 of a minute so revs are 2 and 8 yes

No need to check E and verify B as the question can only have correct answer…

OA D (12secs)

If you want a trick answer….here it goes

Difference of revolutions between P & Q = 30revs/minute

Only 12secs (among answer choices) would give 6 revs {(12/60)*30} and obviously the other is zero giving a lead of 6 revs…..

Hope this helps !!!
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Re: GMAT Prep Question &nbs [#permalink] 13 Aug 2010, 02:17

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