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Tips and Tricks

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Senior Manager
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 70 [0], given: 6

Tips and Tricks [#permalink]  28 Jul 2009, 04:10
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I was wondering if there are any tips or tricks to save time in questions like these rather than manually calculating values. I know one trick which is used to check the greater values in fractions

For e.g to check which one greater among say 2/3 , 3/16 and 7/ 48

Just multiply the denominator one fraction to other numerator i.e 2 x 16 and 3 x 3. here 2x16 is greater hence the 2/3 is greater than 3/16.

Folks please share if you know tips and tricks to save time while doing these cheesy time consuming calculations.

Thanks
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Manager
Joined: 03 Jul 2009
Posts: 107
Location: Brazil
Followers: 2

Kudos [?]: 47 [9] , given: 13

Re: Tips and Tricks [#permalink]  28 Jul 2009, 12:16
9
KUDOS
I have taken 15 seconds to resolve this problem! For this problem specifically, there are some very fast tricks that you can do remembering the properties of recurring decimals. You just need a little patience to understand a first time. Then you probably will never forget.

Here is a brief description useful in a some GMAT exercises:

First - We use the number that is repeating and the denominator has as many "9" digits as there are different digits in the block that repeats. e.g.
0.555555 = 5/9
0.13131313 = 13/99
0.432432432432 = 432/999

Second - If the sequence starts to repeat after some zeros, add the same number of zeros in the denominator. e.g.
0.005555 = 5/900
0.013131313 = 13/990
0.0004324324324... = 432/999000 = 54/124875 = 2/4625

Third - Terminating decimals + Repeating Decimals. e.g.
2.31555555 = 2.31 + 0.00555555 = 231/100 + 5/900
0.745454545 = 0.7 + 0.0454545 = 7/10 + 45/990

Last one - The reciprocal of a prime number "p", except 2 and 5, has a repeating sequence of p-1 digits, or a factor of p-1 digits. e.g.
1/7 = 0.142857 142857 142857... - As you can notice, the sequence has 6 digits = p-1 = 7-1 = 6 digits.
And if you multiply this fraction by a number you will only change the beginning of the sequence. e.g.
4/7 = 4*1/7 = 0.57 142857 142857 ...

****************
Once you have all these little rules in mind it is very fast to work in this problem.
A) 2/11 -> 11 is a factor of 99, so there are 2 repeating digits.
B) 1/3 -> 3 is a factor of 9, so there is 1 repeating digit.
C) 41/99 -> 99, so there are 2 repeating digits.
D) 2/3 -> 3 is a factor of 9, so there is 1 repeating digit..
E) 23/37 -> As I still don't have one item that is winning in repeating digits, this must be CORRECT

E

Good studies!

If you enjoyed the post, please consider a kudo!!! I need to practice my verbal skills in the GMATClub tests

Last edited by coelholds on 28 Jul 2009, 13:55, edited 2 times in total.
Senior Manager
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 70 [1] , given: 6

Re: Tips and Tricks [#permalink]  28 Jul 2009, 12:25
1
KUDOS
coelholds wrote:
I have taken 15 seconds to resolve this problem! For this problem specifically, there are some very fast tricks that you can do remembering the properties of recurring decimals. You just need a little patience to understand a first time. Then you probably will never forget.

Here is a brief description useful in a some GMAT exercises:

First - We use the number that is repeating and the denominator has as many "9" digits as there are different digits in the block that repeats. e.g.
0.555555 = 5/9
0.13131313 = 13/99
0.432432432432 = 432/999

Second - If the sequence starts to repeat after some zeros, add the same number of zeros in the denominator. e.g.
0.005555 = 5/900
0.013131313 = 13/990
0.0004324324324... = 432/999000 = 54/124875 = 2/4625

Third - Terminating decimals + Repeating Decimals. e.g.
2.31555555 = 2.31 + 0.00555555 = 231/100 + 5/900
0.745454545 = 0.7 + 0.0454545 = 7/10 + 45/990

Last one - The reciprocal of a prime number "p", except 2 and 5, has a repeating sequence of p-1, or a multiple of p-1. e.g.
1/7 = 0.142857 142857 142857... - As you can notice, the sequence has 6 digits = p-1 = 7-1 = 6 digits.
And if you multiply this fraction by a number you will only change the beginning of the sequence. e.g.
4/7 = 4*1/7 = 0.57 142857 142857 ...

****************
Once you have all these little rules in mind it is very fast to work in this problem.
A) 2/11 -> 11 is a factor of 99, so there are 2 repeating digits.
B) 1/3 -> 3 is a factor of 9, so there is 1 repeating digit.
C) 41/99 -> 99, so there are 2 repeating digits.
D) 2/3 -> 3 is a factor of 9, so there is 1 repeating digit..
E) 23/37 -> As I still don't have one item that is winning in repeating digits, this must be CORRECT

E

Good studies!

If you enjoyed the post, please consider a kudo!!! I need to practice my verbal skills in the GMATClub tests

Thanks coelholds, That was nice.. ! +1 for this one .. without knowing these tricks I spent almost 1.5 min.
Manager
Joined: 03 Jul 2009
Posts: 107
Location: Brazil
Followers: 2

Kudos [?]: 47 [2] , given: 13

Re: Tips and Tricks [#permalink]  29 Jul 2009, 05:25
2
KUDOS
You are welcome and thanks
Senior Manager
Joined: 16 Apr 2009
Posts: 252
Schools: Ross
Followers: 1

Kudos [?]: 18 [0], given: 10

Re: Tips and Tricks [#permalink]  29 Jul 2009, 06:25
vivid explanations.
+1 from me..

Please post tips and tricks like these. you'll be flooded with kudos!!!
_________________

Keep trying no matter how hard it seems, it will get easier.

Re: Tips and Tricks   [#permalink] 29 Jul 2009, 06:25
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