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Donovan and Michael are racing around a circular 400-meter track. If D

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Carcass
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Donovan and Michael are racing around a circular 400-meter track. If D [#permalink] New post   19 Apr 2021, 03:51
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Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?

A. 8
B. 9
C. 10
D. 11
E. 12

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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B
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Re: Donovan and Michael are racing around a circular 400-meter track. If D [#permalink] New post   19 Apr 2021, 06:21
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Carcass wrote:
Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?

A. 8
B. 9
C. 10
D. 11
E. 12

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book


If Michael passes Donovan, then Donovan completes ONE LAP LESS than Michael completes IN THE SAME AMOUNT OF TIME.
So, if x = # of laps Michael completes, then....
x - 1 = # of laps Donovan completes.

So, we can write the following WORD EQUATION:
(time for Michael to complete x laps) = (time for Donovan to complete x - 1 laps)
It takes 40 seconds for Michael to complete EACH lap, and it takes 45 seconds for Donovan to complete EACH lap.
So, we get: (40)(x) = (45)(x - 1)
Expand: 40x = 45x - 45
Solve to get x = 9

So, Michael must complete 9 laps

Answer: B

Cheers,
Brent
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Chaithraln2499
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Re: Donovan and Michael are racing around a circular 400-meter track. If D [#permalink] New post   31 Jan 2022, 06:12
Can we expect such questions in GRE exam?

GreenlightTestPrep wrote:
Carcass wrote:
Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?

A. 8
B. 9
C. 10
D. 11
E. 12

Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book


If Michael passes Donovan, then Donovan completes ONE LAP LESS than Michael completes IN THE SAME AMOUNT OF TIME.
So, if x = # of laps Michael completes, then....
x - 1 = # of laps Donovan completes.

So, we can write the following WORD EQUATION:
(time for Michael to complete x laps) = (time for Donovan to complete x - 1 laps)
It takes 40 seconds for Michael to complete EACH lap, and it takes 45 seconds for Donovan to complete EACH lap.
So, we get: (40)(x) = (45)(x - 1)
Expand: 40x = 45x - 45
Solve to get x = 9

So, Michael must complete 9 laps

Answer: B

Cheers,
Brent
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Carcass
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Re: Donovan and Michael are racing around a circular 400-meter track. If D [#permalink] New post   31 Jan 2022, 06:20
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I believe yes
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GreenlightTestPrep
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Re: Donovan and Michael are racing around a circular 400-meter track. If D [#permalink] New post   31 Jan 2022, 06:28
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Chaithraln2499 wrote:
Can we expect such questions in GRE exam?


This question is well within the scope of the GRE.
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Paul121
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Re: Donovan and Michael are racing around a circular 400-meter track. If D [#permalink] New post   24 Sep 2023, 12:38
GreenlightTestPrep

I thought about this problem from another point, and I always get 8.
Where I am wrong, if I am?

Step 1: Find Speeds
Donovan speed in minutes:
400/45 -> (400*3)/4

Michael speed in minutes:
400/40 -> (400*2)/3

Step 2: Find the speed difference
(400*3)/4 - (400*2)/3 = 100/3

Step 3: Find how many minutes it will take to finish 400 meters circle with 100/3 speed
400 / (100/3) = 12 minutes

Step 4: How many meters Michael drive in 12 minutes
( (400*2)/3 ) * 12 = 3,200

Step 5: Find how many 400-meter circles we have in 3,200 meters
3,200 / 400 = 8

Final Result:
Michael drove 8 circles.

Donovan has one extra circle so he had 9, but the question asks about Michael.

Am I wrong about my approach?
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sachin27
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Re: Donovan and Michael are racing around a circular 400-meter track. If D [#permalink] New post   04 Jan 2024, 00:02
simpler solution would be to find common multiples of 45 and 40,
45*8 = 360
40*9 = 360

hence, it would take 9 laps.
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