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Re: Circular gears P and Q start rotating at the same time at
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16 Mar 2017, 06:39
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.



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Re: Circular gears P and Q start rotating at the same time at
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21 Mar 2017, 06:24
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
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Re: Circular gears P and Q start rotating at the same time at
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28 Mar 2017, 11:05
let's translate into seconds: P: 1/6 per second Q: 2/3 per second we can make the following equation: P*S=Q*S6 6=s(qp) 6=s*1/2 s=12 Answer is D



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Re: Circular gears P and Q start rotating at the same time at
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18 Jul 2017, 17:59
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



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Re: Circular gears P and Q start rotating at the same time at
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16 Aug 2017, 09:38
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..



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Re: Circular gears P and Q start rotating at the same time at
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13 Nov 2017, 17:10
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. BunuelI 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!!!



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Re: Circular gears P and Q start rotating at the same time at
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13 Nov 2017, 18:41
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. BunuelI 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



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Re: Circular gears P and Q start rotating at the same time at
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28 Nov 2017, 19:24
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



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Re: Circular gears P and Q start rotating at the same time at
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28 Nov 2017, 20:06
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) = ?
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Re: Circular gears P and Q start rotating at the same time at
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17 Jan 2018, 03:14
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!



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Re: Circular gears P and Q start rotating at the same time at
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28 Feb 2018, 22:23
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
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Re: Circular gears P and Q start rotating at the same time at
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15 Mar 2018, 22:53
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 = 2/31/6 = 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.



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Re: Circular gears P and Q start rotating at the same time at
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18 Apr 2018, 09:17
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….
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Re: Circular gears P and Q start rotating at the same time at
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10 Sep 2018, 19:41
Bunuel, can you share more such questions ?



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Re: Circular gears P and Q start rotating at the same time at
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Re: Circular gears P and Q start rotating at the same time at
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16 Oct 2018, 01:55
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 2/31/6=1/2 rev/sec
There time taken to cover 6 rev = 6 /(1/2) = 12 seconds
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Re: Circular gears P and Q start rotating at the same time at
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13 Feb 2019, 06:53
RATEtimedistance P:10 x/10 x Q:40(x+6)/40x+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???



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Re: Circular gears P and Q start rotating at the same time at
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13 Feb 2019, 19:54
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
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Re: Circular gears P and Q start rotating at the same time at
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07 Aug 2019, 11:17
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 = QP = 2/3  1/6 =(41)/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
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