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Quick way needed: fractions

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Quick way needed: fractions

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?

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Last edited by clawhammer on Sun Nov 28, 2010 7:49 am, edited 1 time in total.
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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
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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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by goyalsau » Sun Nov 28, 2010 7:21 am
I was not able to read your last line, :|
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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 ?
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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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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.
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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! :)
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or visit my blog:
https://realusefulgmat.blocked/
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by clawhammer » Sun Nov 28, 2010 8:04 am
Source is Grockit.
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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.
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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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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!
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