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?
6
8
10
12
15
d
Rates - Word problem
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
One approach is to use equivalent ratios.outty 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?
6
8
10
12
15
We know that, for every 60 seconds, Q makes 30 more revolutions than P does.
We want to determine how many seconds it will take Q to make 6 more revolutions than P does.
We may immediately see that it will take 1/5 the time (i.e., 12 seconds), but let's use equivalent ratios.
The ratio will be: (# of seconds)/(# of extra revolutions Q makes).
So, we get: 60/30 = x/6
Cross multiply to get 30x = (60)(6)
x = 12
In other words, it will take 12 seconds.
Cheers,
Brent
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi outty,
This type of Rate question can be answered in a number of different ways (beyond the various "math approaches", you can also TEST THE ANSWERS).
Here's a math approach that isolates each additional rate:
Gear P = 10 revolutions per minute = 1 revolution every 6 seconds
Gear Q = 40 revolutions per minute = 1 revolution every 1.5 seconds
In 6 seconds:
Gear P = 1 revolution
Gear Q = 4 revolutions
Difference = 4 - 1 = Gear Q does 3 MORE revolutions per 6 seconds than Gear P does.
The question asks how long it will take for Gear Q to do 6 MORE revolutions than Gear P, so we double the above result:
6 seconds x 2 = 12 seconds.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This type of Rate question can be answered in a number of different ways (beyond the various "math approaches", you can also TEST THE ANSWERS).
Here's a math approach that isolates each additional rate:
Gear P = 10 revolutions per minute = 1 revolution every 6 seconds
Gear Q = 40 revolutions per minute = 1 revolution every 1.5 seconds
In 6 seconds:
Gear P = 1 revolution
Gear Q = 4 revolutions
Difference = 4 - 1 = Gear Q does 3 MORE revolutions per 6 seconds than Gear P does.
The question asks how long it will take for Gear Q to do 6 MORE revolutions than Gear P, so we double the above result:
6 seconds x 2 = 12 seconds.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi outty,
Since I mentioned TESTing THE ANSWERS, here's how that approach would work.
We know the rates of the two gears, so if we were given the amount of time, we COULD figure out the number of revolutions that each Gear made.
Converting the rates into seconds gives us:
Gear P = 10/60 = 1/6 revolution per second
Gear Q = 40/60 = 2/3 revolution per second
Answer B: 8 seconds
In 8 seconds,
Gear P makes 8(1/6) = 1 1/3 revolutions
Gear Q makes 8(2/3) = 5 1/3 revolutions
Difference = 4 revolutions. This is TOO LOW (it's supposed to be exactly 6 revolutions), so we need more time...
Eliminate A and B.
Answer D: 12 seconds
In 12 seconds,
Gear P makes 12(1/6) = 2 revolutions
Gear Q makes 12(2/3) = 8 revolutions
Difference = 6 revolutions. This is EXACTLY what it's supposed to be. We've found the match, so we're done.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
Since I mentioned TESTing THE ANSWERS, here's how that approach would work.
We know the rates of the two gears, so if we were given the amount of time, we COULD figure out the number of revolutions that each Gear made.
Converting the rates into seconds gives us:
Gear P = 10/60 = 1/6 revolution per second
Gear Q = 40/60 = 2/3 revolution per second
Answer B: 8 seconds
In 8 seconds,
Gear P makes 8(1/6) = 1 1/3 revolutions
Gear Q makes 8(2/3) = 5 1/3 revolutions
Difference = 4 revolutions. This is TOO LOW (it's supposed to be exactly 6 revolutions), so we need more time...
Eliminate A and B.
Answer D: 12 seconds
In 12 seconds,
Gear P makes 12(1/6) = 2 revolutions
Gear Q makes 12(2/3) = 8 revolutions
Difference = 6 revolutions. This is EXACTLY what it's supposed to be. We've found the match, so we're done.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
When elements compete, SUBTRACT THEIR RATES.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?
6
8
10
12
15
Here:
Time = (desired number of additional revolutions)/(Q's rate - P's rate).
Since Q must make 6 MORE REVOLUTIONS than P, we get:
6/(40-10) = 1/5 of a minute = 12 seconds.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3