Circular gears L and R start to rotate at the same time...

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BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Jan 29, 2018 6:37 am

circular gears L and R start to rotate at the same time at the same rate. Gear L makes complete 10 revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?

A. 6
B. 8
C. 10
D. 12
E. 15

The OA is D.

I'm really confused with this PS question.

I know the rate for each gear,

Gear L, 10 revolutions per minute or 1/6 revolution per second.

Gear R, 40 revolutions per minute or 2/3 revolution per second.

But, I don't understand what can I do to complete the solution. Experts, any suggestion? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Mon Jan 29, 2018 6:37 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Mon Jan 29, 2018 10:16 am

Think about the number of revolutions as a "distance" traveled. So in one minute, one will have gone 10 revolutions and the other 40.

Thinking about it this way, you can use the Distance = Rate x Time formula

Call X the distance L travels = 10 * T

Call Y the distance R travels = 40*T

The problem asks for time it takes for R to "travel" 6 more rotations than L. Using the X and Y above, this means:

Y - X= 6 = 40*T - 10*T = T*30

therefore T =1/5 minute or 12, D

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jan 29, 2018 12:09 pm

LUANDATO wrote:circular gears L and R start to rotate at the same time at the same rate. Gear L makes complete 10 revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?

A. 6
B. 8
C. 10
D. 12
E. 15

When elements compete, SUBTRACT THEIR RATES.

Every minute R makes 40 revolutions and L makes 10 revolutions.
The difference between their rates is 40-10 = 30.
Thus, every minute R makes 30 more revolutions than L.

To determine how many seconds it will take R to make 6 more revolutions than L, set up a proportion:
30 revolutions/60 seconds = 6 revolutions/x seconds
30x = 360
x = 12.

The correct answer is D.

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Wed Jan 31, 2018 6:54 am

GMATGuruNY wrote:
LUANDATO wrote:circular gears L and R start to rotate at the same time at the same rate. Gear L makes complete 10 revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?

A. 6
B. 8
C. 10
D. 12
E. 15
When elements compete, SUBTRACT THEIR RATES.

Every minute R makes 40 revolutions and L makes 10 revolutions.
The difference between their rates is 40-10 = 30.
Thus, every minute R makes 30 more revolutions than L.

To determine how many seconds it will take R to make 6 more revolutions than L, set up a proportion:
30 revolutions/60 seconds = 6 revolutions/x seconds
30x = 360
x = 12.

The correct answer is D.

Dear Mitch,
When Di you consider them competing? they are meshed together so they have opposite as if cars coming from opposite ways. Hence, it should be Addition.

where did I go wrong here?

thanks

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

gears

by GMATGuruNY » Wed Jan 31, 2018 8:44 am

Mo2men wrote:Dear Mitch,
When Di you consider them competing? they are meshed together so they have opposite as if cars coming from opposite ways. Hence, it should be Addition.

The prompt does not indicate that the gears are interlocking.
The problem above is virtually the same as the following:

L is running around a circular track at a rate of 10 laps per minute. R is running around a different circular track at a rate of 40 laps per minute. If L and R start to run at the same time, how many seconds will it take R to complete 6 more laps than L?

In each case, R is COMPETING with L to complete 6 more revolutions than L in a given amount of time.

Last edited by GMATGuruNY on Wed Jan 31, 2018 12:27 pm, edited 1 time in total.

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DrMaths: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Mon Jan 15, 2018 2:01 am

by DrMaths » Wed Jan 31, 2018 9:35 am

No need to consider summing or subtracting rates; just look at comparing ratios in a simple equation:
L/R = 10/40 = 1/4 = L/(L+6)
Rearranged gives
L+6 = 4L
3L= 6
L = 2 (no. of revolutions)
as L makes 10 revs per minute, then 2 revs is 2/10 of a minute = 1/5 of a minute
1/5 of 60 seconds = 12 seconds

A. 6
B. 8
C. 10
D. 12
E. 15

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Jan 31, 2018 4:22 pm

LUANDATO wrote:circular gears L and R start to rotate at the same time at the same rate. Gear L makes complete 10 revolutions per minute and gear R makes 40 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 6 more revolutions than gear L?

A. 6
B. 8
C. 10
D. 12
E. 15

As we can see, Gear R makes 30 more revolutions per minute than Gear L does. So, we can set up the following proportion to solve for the time it takes Gear R to make 6 more revolutions than Gear L 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 multiplying, we have:

30x = 360

x = 12

D

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