terminating decimal?

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

terminating decimal?

by uptowngirl92 » Sat Sep 05, 2009 3:07 am

Is r/s^2 a terminating decimal?
s=225
r=81

OA:C

Hey guys i had thot that i had finally gotten the terminating decimal thing down.Apparently not.

I distinctly remember that to find out whether a fraction is terminating or nor all we need is the denominator.The numerator has no role in it.
So from the first stmt we know that since 225 does not contain ONLY 2's and 5's it will not result in a terminationg decimal...Suff.

Stmt 2 is insuff.
Please help

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Source: Beat The GMAT — Data Sufficiency | Sat Sep 05, 2009 3:07 am

fightthegmat: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Wed Jan 14, 2009 11:45 am; Thanked: 1 times; GMAT Score:600

by fightthegmat » Sat Sep 05, 2009 4:53 am

IMO : C

1)Well s = 225.
225 = 3*5*3*5
No info abt numerator. You need to know the value in numerator because sometimes some value may cancel with the denominator.

Stm 2) It gives you r = 81
81 = 3*3*3*3

So now ,Num/den gives you two 5's in the denominator which gives you a terminating decimal.

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Nermal: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Sun Jun 21, 2009 10:25 am; Location: Germany; Thanked: 7 times

by Nermal » Sat Sep 05, 2009 5:46 am

what is a terminating decimal?

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qwe12: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Sat May 30, 2009 11:22 am; Thanked: 2 times

Re: terminating decimal?

by qwe12 » Sun Sep 06, 2009 12:00 am

uptowngirl92 wrote:Is r/s^2 a terminating decimal?
s=225
r=81

Just consider r/s instead of (r/s)^2. Because if r/s is terminating then (r/s)^2 will be terminating.

(1)

1/225 = 0.004444444..... Is (r/s)^2 terminating? NO
2/225 = 0.008888888..... Is (r/s)^2 terminating? NO
...
225/225 = 1 Is (r/s)^2 terminating? YES

Not Sufficient

(2)
81/81 = 1 Is (r/s)^2 terminating? YES
81/7 = 11.5714286... Is (r/s)^2 terminating? NO

Not Sufficient

(1) and (2)

81/225 = 9/25 = 0.36 Is (r/s)^2 terminating? YES

(C)

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

Re: terminating decimal?

by Ian Stewart » Sun Sep 06, 2009 5:48 am

uptowngirl92 wrote:Is r/s^2 a terminating decimal?
s=225
r=81

OA:C

Hey guys i had thot that i had finally gotten the terminating decimal thing down.Apparently not.

I distinctly remember that to find out whether a fraction is terminating or nor all we need is the denominator.The numerator has no role in it.
So from the first stmt we know that since 225 does not contain ONLY 2's and 5's it will not result in a terminationg decimal...Suff.

Stmt 2 is insuff.
Please help

I've posted about terminating decimals elsewhere, but the numerator can sometimes be important. To check if a decimal terminates:

1. Reduce your fraction completely (here, the numerator may be important, because some primes may cancel from both the numerator and denominator)

2. Once your fraction is reduced, the numerator is irrelevant. If the only prime divisors of the denominator are 2, 5 or both, the decimal will terminate. If there are any other prime divisors of the denominator, the decimal will repeat/recur.

If s = 225, then the denominator of the fraction above is divisible by 3. However, we don't know if the fraction is reduced; perhaps all the 3's cancel. So we can't be certain from Statement 1 whether the decimal terminates. Statement 2 tells us nothing about the denominator, so is not sufficient. Using both Statements, we know the exact value of the fraction, so of course we can determine whether it terminates; there's no need to actually answer the question.

And to answer Nermal's question, a terminating decimal is one that stops, i.e. one that could be written down completely on a finite piece of paper. So 0.53, 5.662 and 0.0003 are all terminating decimals, for example. The decimal 0.3333.... continuing forever (which is equal to 1/3) is not terminating, since it does not stop; such a decimal is called a 'repeating' or 'recurring' decimal.

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

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