Is there a faster way to do this problem(p.155 qu.22 OG11th)

[jsoana]

22. If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits?

A) 2/11

B) 1/3

C) 41/99

D) 2/3

E) 23/37

-----------------------
Now I know 1/3 and 2/3 : 0.33333r & 0.666666r but the others I calculated via long division, and the book did the same but man that is just unnecessarily time consuming. Surely there is a trick I am missing?

Jeremy.

Since this is my first post I also want to know if people have found errors in OG 11th because i have found 2 already and I'm not far in. (p.154 qu.20 & p.155 q 28 B) should read y/x)

[Ian Stewart]

22. If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits?

A) 2/11

B) 1/3

C) 41/99

D) 2/3

E) 23/37

-----------------------
Now I know 1/3 and 2/3 : 0.33333r & 0.666666r but the others I calculated via long division, and the book did the same but man that is just unnecessarily time consuming. Surely there is a trick I am missing?

Jeremy.

You can rule out 1/3 and 2/3 quickly, as you've done. If you notice that the denominators 11 and 99 are related, you can use that to your advantage. If you, say, long divide to find that

2/11 = 0.18181818...

then 1/11 must be half of that:

1/11 = 0.09090909...

and 1/99 must be 1/9th of that:

1/99 = 0.0101010101

and 41/99 is 41 times that:

41/99 = 0.41414141

Since 41/99 and 2/11 both have a repeating pattern of two digits, and 1/3 and 2/3 have a repeating pattern of one digit, 23/37 must have a pattern of three or more repeating digits - otherwise the question would have more than one right answer, which never happens on the GMAT.

Since this is my first post I also want to know if people have found errors in OG 11th because i have found 2 already and I'm not far in. (p.154 qu.20 & p.155 q 28 B) should read y/x)

You must have the (older) uncorrected edition. If you google "official guide gmat corrections", you should be able to find the pdf issued by GMAC which lists the errata in the book. Later printings of the book fix these errors, so most people won't need that pdf.

[jsoana]

Thank you so much, that is mighty ingenious, just wish i could have seen that too Hopefully that will come with practice.

With regards to the book, I am really quite annoyed since I just purchased this off amazon a couple weeks ago.

Thanks again for your help.

Jeremy

[raunekk]

that was Ian enlightening us....


just 2 good..