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number properties

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Source: — Data Sufficiency |
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by user123321 » Fri Jan 13, 2012 6:19 am
sud21 wrote:R and S are integers, is R/S a finite decimal?
1). R is the factor of 100
2). S is the factor of 100
1) has no info about S. hence insuff.
2) has no info about R. hence insuff.

using both,
still we cannot determine whether it is finite decimal or not.
because for example, R can be 200 and S can be 300.

[spoiler]IMO E?[/spoiler]

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by sam2304 » Fri Jan 13, 2012 5:06 pm
user123321 wrote:
sud21 wrote:R and S are integers, is R/S a finite decimal?
1). R is the factor of 100
2). S is the factor of 100
1) has no info about S. hence insuff.
2) has no info about R. hence insuff.

using both,
still we cannot determine whether it is finite decimal or not.
because for example, R can be 200 and S can be 300.

[spoiler]IMO E?[/spoiler]

user123321
200/300 are multiples of 100.

2 * 2 * 5 * 5 = 100
2, 4, 5, 10, 20, 25, 50 are all factors and any of the values divided by another will be a finite decimal. In short any value divided by above numbers will be a finite decimal. So if the denominator has above values it will be suffice.

IMO B.
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by Neo Anderson » Fri Jan 13, 2012 6:33 pm
any value divided by above numbers will be a finite decimal
sam can you pls discuss the property of terminating rational numbers! I seem to have missed an important point here.

Because I picked C as the answer, in that numerator and denominator both are factors of 100 and you get a finite rational number!
but as you said, numerator can be any thing, not necessarily a factor of 100. how's that??
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by sam2304 » Fri Jan 13, 2012 8:59 pm
Neo Anderson wrote:
any value divided by above numbers will be a finite decimal
sam can you pls discuss the property of terminating rational numbers! I seem to have missed an important point here.

Because I picked C as the answer, in that numerator and denominator both are factors of 100 and you get a finite rational number!
but as you said, numerator can be any thing, not necessarily a factor of 100. how's that??
I am not sure if i can point out the right property here, but any whole number when divided by 2 or/and 5 will always result in a terminating decimal and other factors here are just multiples of them.
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by shankar.ashwin » Fri Jan 13, 2012 9:56 pm
The answer is B here.

Value of R doesnt matter as long as you know the denominator is either 2 or 5 or contains only factors of 2 and 5 (or factors of 2 alone or 5 alone)

For eg;

1/2 = 0.5
1/3 = 0.333
1/4 = 1/2^2 = 0.25
1/5 = 0.2
1/6 = 0.1666
1/7 = 0.1428...
1/8 = 1/2^3 = 0.125
1/9 = 0.111..
1/10 = 1/2*5 = 0.1

and so on. So its sufficient S = 100 = 2^2*5^2
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by sam2304 » Sat Jan 14, 2012 12:47 am
Found this in wiki.
A decimal representation written with a repeating final 0 is said to terminate before these zeros. Instead of "1.585000..." one simply writes "1.585". The decimal is also called a terminating decimal. Terminating decimals represent rational numbers of the form k/(2^n5^m). For example, 1.585 = 317/200 = 317/(2352).
https://en.wikipedia.org/wiki/Repeating_decimal
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by ArunangsuSahu » Sat Jan 14, 2012 8:44 am
Statement 1:

INSUFFICIENT as we don't know S

Statement 2:

100 has factors as 1,2,4,5,10,20,25,50,100

2 and 5 will never give a terminating decimal

So neither of the resultant factors

(B) is sufficient
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