Quick way needed: fractions

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clawhammer: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Aug 15, 2010 10:08 amFollowed by: 1 member; Thanked: 3 times

by clawhammer » Sun Nov 28, 2010 7:02 am

Please tell me what is a quick way to solve this and be confident of the answer?

A 100-meter sprinting track is marked of in sixths (the larger marks in the illustration) and in eighths (the smaller marks). What is the shortest approximate distance, in meters, between any two of the marks?

I mean, i do not want to try out many fractions randomly to possibly find the smallest. Anyway to quickly determine which two to subtract?

Last edited by clawhammer on Sun Nov 28, 2010 7:49 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Sun Nov 28, 2010 7:02 am

goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Sun Nov 28, 2010 7:19 am

clawhammer wrote:Please tell me what is a quick way to solve this and be confident of the answer?

A 100-meter sprinting track is marked of in sixths (the larger marks in the illustration to the left) and in eighths (the smaller marks). What is the shortest approximate distance, in meters, between any two of the marks?

I mean, i do not want to try out many fractions randomly to possibly find the smallest. Anyway to quickly determine which two to subtract?

1/6 = 16.66
2/6 , = 32.33
3/6 = 50
4/6 = 76.66
5/6 = 83.33

1/8 = 12.50
2/8 = 25
3/8 = 37.5
4/8 = 50

By this we can see that the shortest distance will be 1/6 - 1/8 = 1/24 = 4.16

Saurabh Goyal
[email protected]
-------------------------

EveryBody Wants to Win But Nobody wants to prepare for Win.

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clawhammer: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Aug 15, 2010 10:08 amFollowed by: 1 member; Thanked: 3 times

by clawhammer » Sun Nov 28, 2010 7:21 am

And you are supposed to know the values of all those fractions? ** gulp **

Anything easier bro?

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Sun Nov 28, 2010 7:21 am

I was not able to read your last line,

Saurabh Goyal
[email protected]
-------------------------

EveryBody Wants to Win But Nobody wants to prepare for Win.

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beat_gmat_09: Master | Next Rank: 500 Posts; Posts: 437; Joined: Sat Nov 22, 2008 5:06 amFollowed by: 1 member; Location: India; Thanked: 50 times; GMAT Score:580

by beat_gmat_09 » Sun Nov 28, 2010 7:42 am

clawhammer wrote:And you are supposed to know the values of all those fractions? ** gulp **

Anything easier bro?

Even i would want to know, any quicker method guys ?

Hope is the dream of a man awake

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clawhammer: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Aug 15, 2010 10:08 amFollowed by: 1 member; Thanked: 3 times

by clawhammer » Sun Nov 28, 2010 7:51 am

I didn't attach the image first, cuz i didn't care as much. Now it seems reasonable to have it. Actually the image allows you to quickly shortlist a few fractions. I guess this is the shortest way? Didn't take the image into so much consideration when I did it the first time.

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beat_gmat_09: Master | Next Rank: 500 Posts; Posts: 437; Joined: Sat Nov 22, 2008 5:06 amFollowed by: 1 member; Location: India; Thanked: 50 times; GMAT Score:580

by beat_gmat_09 » Sun Nov 28, 2010 7:59 am

clawhammer wrote:I didn't attach the image first, cuz i didn't care as much. Now it seems reasonable to have it. Actually the image allows you to quickly shortlist a few fractions. I guess this is the shortest way? Didn't take the image into so much consideration when I did it the first time.

What's the source ?
May happen, image won't be provided in actual exam, then a quicker method is needed.

Hope is the dream of a man awake

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Laura GMAT Tutor: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Tue Nov 23, 2010 9:44 amFollowed by: 6 members; Thanked: 16 times; GMAT Score:780

by Laura GMAT Tutor » Sun Nov 28, 2010 8:02 am

Someone asked, "Do I really need to memorize all those fractions?"

My answer is, yes.

Listen, my friends. Many of you spend hours on these forums trying to do the hardest possible questions you can possibly find. So obviously you're dedicated. Instead of focusing on those untestlike questions, here's some small thing you can do that will have immediate and obvious benefits. Learn your sixths and eights!

You'll be glad you did.

follow me on twitter!

@LauraGMATtutor

or visit my blog:
https://realusefulgmat.blocked/

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clawhammer: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Aug 15, 2010 10:08 amFollowed by: 1 member; Thanked: 3 times

by clawhammer » Sun Nov 28, 2010 8:04 am

Source is Grockit.

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sun Nov 28, 2010 9:12 am

First of all this question is much easier than others of this type.
It is obvious from the image (and also from goyalsau's list of fractions) that both types of marks coincide on '50'. Thus shortest possible distance is zero!

Now if you are looking for a method to solve this kind of problems here is one: https://www.beatthegmat.com/fifths-seven ... tml#313084

Following the method as discussed in the above mentioned post, this question asks for what is shortest possible distance between the multiples of 100/6 and 100/8. Now LCM of 100/6 and 100/8 is 100/2 = 50. Range of the multiples is 100, which is greater than 50. Thus the shortest possible distance is zero!

Hope that helps.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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clawhammer: Master | Next Rank: 500 Posts; Posts: 132; Joined: Sun Aug 15, 2010 10:08 amFollowed by: 1 member; Thanked: 3 times

by clawhammer » Sun Nov 28, 2010 9:23 am

Rahul@gurome wrote:
Following the method as discussed in the above mentioned post, this question asks for what is shortest possible distance between the multiples of 100/6 and 100/8. Now LCM of 100/6 and 100/8 is 100/2 = 50. Range of the multiples is 100, which is greater than 50. Thus the shortest possible distance is zero!

Hope that helps.

Rahul, could you please explain, how to find this RANGE OF MULTIPLES?

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GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sun Nov 28, 2010 10:42 am

clawhammer wrote:Rahul, could you please explain, how to find this RANGE OF MULTIPLES?

"A 100-meter sprinting track is marked of in sixths and in eighths."

The marks (multiples) are from 0 meter to 100 meter. Thus range of the multiples is 100!

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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