easy way

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blaster: Master | Next Rank: 500 Posts; Posts: 233; Joined: Mon Jun 09, 2008 1:30 am; Thanked: 5 times

by blaster » Thu Sep 03, 2009 4:36 am

Which of the following fractions is equal ot the decimal 0.0625

A) 5/8
B) 3/8
C) 1/16
D) 1/18
E) 3/80

is there easy way to solve this kind of question?

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Source: Beat The GMAT — Problem Solving | Thu Sep 03, 2009 4:36 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Thu Sep 03, 2009 4:58 am

The decimal can be rewritten as:

0.0625 = 625/10 000

Now, if you know your perfect squares, this one will be easy. 625 = 25^2 and 10 000 = 100 * 100 = 25 * 4 * 100 = 25 * 400

So you have:

625/10 000 = 25*25/25*400 = 25/400 = 25/4*4*25 = 1/4*4 = 1/16.

I guess it's down to how well you can work with decimals.

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: easy way

by Ian Stewart » Thu Sep 03, 2009 2:29 pm

blaster wrote:Which of the following fractions is equal ot the decimal 0.0625

A) 5/8
B) 3/8
C) 1/16
D) 1/18
E) 3/80

is there easy way to solve this kind of question?

There are a few ways to do this kind of question. I'd personally likely go with Dana's approach, but with the answer choices above, there are other options. 5/8 and 3/8 are clearly larger than 0.1, so cannot be correct. 3/80 is between 3/100 = 0.03 and 3/50 = 0.06, so is too small. 1/18 is a reduced fraction with a prime divisor different from 2 or 5 in its denominator, so it would yield a repeating decimal, so can't possibly be equal to 0.0625. That only leaves 1/16 as a possibility.

You might also be able to use a few decimals you already know to work out the decimal equivalents of the fractions above. For example, 1/4 is equal to 0.25; 1/8 is half of 1/4, so must equal half of 0.25, or 0.125. So 3/8 is three times 0.125, or 0.375, and 3/80 is one tenth of that, so is equal to 0.0375. Similarly, we can find that 5/8 = 0.625. To find the decimal for 1/18, we can use the fact that 1/3 = 0.333..., and since 1/9 is one third of 1/3, 1/9 must be equal to 1/3 of 0.333..., so 1/9 = 0.111... Now, 1/18 is one half of that, so 1/18 = 0.0555....

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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