recurring decimal

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Mar 03, 2009 4:55 am

The value of the recurring decimal number 0.6313131... is equal to

A. 65/106
B. 125/198
C. 627/990
D. 691/1124
E. 737/1200

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Source: Beat The GMAT — Problem Solving | Tue Mar 03, 2009 4:55 am

Baldini: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon Mar 02, 2009 6:06 am; Thanked: 3 times

by Baldini » Tue Mar 03, 2009 5:46 am

Answer is B.
So you by any chance know a shortcut for this type of exercise?
thx

GMAX

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bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

by bluementor » Tue Mar 03, 2009 5:55 am

0.631313131....
= 0.6 + 0.0303030303.. + 0.001010101...
= 0.6 + 3/99 + 0.001010101...
= 0.6 + 3/99 + (0.01010101...)/10
= 0.6 + 3/99 + (1/99)/10
=0.6 + 3/99 + (1/990)
=3/5 + 31/990
=(3(198) + 31)/990
= 625/990
=125/198

Choose B.

-BM-

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Mar 03, 2009 6:05 am

Baldini wrote:Answer is B.
So you by any chance know a shortcut for this type of exercise?
thx

Sure Baldini, if the repeating pattern of digits is set to start right after the decimal point, then this part will be equivalent to the integer formed by pattern divided by as many 9s as are the digits in the numerator; for example 0.861861861... will always be equal to 861/999; 3.057575757... = 3 + 0.057575757... = 3 + (1/10) (0.57575757...) = 3 + (1/10) (57/99) = 3 + (1/10) (19/33) = 3 + (19/330) = 1009/330.

The present number

0.6313131... = 0.6 + 0.0313131... = 6/10 + (1/10) (0.313131...)

= 3/5 + (1/10) (31/99) = 3/5 + 31/990 = [(198*3) + 31]/990

= (594 + 31)/990 = 625/990 = 125/198

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Baldini: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon Mar 02, 2009 6:06 am; Thanked: 3 times

by Baldini » Tue Mar 03, 2009 6:20 am

thanks a lot.

GMAX

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