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If a and b are integers, is the fraction a/b a terminating decimal?

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If a and b are integers, is the fraction a/b a terminating decimal? [#permalink] New post   24 Aug 2020, 03:28
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If \(a\) and \(b\) are integers, is the fraction \(\frac{a}{b}\) a terminating decimal?

(1) \(b\) is a prime numbers less than 7

(2) \(a\) and \(b\) are integers with no common factors other than 1.
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Re: If a and b are integers, is the fraction a/b a terminating decimal? [#permalink] New post   24 Aug 2020, 03:38
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Explanation:

(I) b is a prime numbers less than 7
Prime number less than 7 : 2,3,5
a can be any value ,let a= 1
So, a/b when b =2 : 0.5
a/b when b=3 : 0.3333
Not Sufficient

(II) a and b are integers with no common factors other than 1.
means a,b are both prime numbers.
Let a=2, b=3
a/b = 0.6666
let a=3, b =5
a/b = 0.6
Not Sufficient

From Statement 1 & 2,
Let a=2, b=3
a/b = 0.6666
let a=2, b =5
a/b = 0.4
Not Suffcient

IMO-E
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Re: If a and b are integers, is the fraction a/b a terminating decimal? [#permalink] New post   24 Aug 2020, 06:58
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rajatchopra1994 wrote:
(II) a and b are integers with no common factors other than 1.
means a,b are both prime numbers.


If a and b have no common factor besides 1, that only means their Greatest Common Divisor is 1. It is certainly possible that a and b are different prime numbers, but that does not need to be true -- it could be that a = 10 and b = 21, for example.

Otherwise your solution is perfect.
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Re: If a and b are integers, is the fraction a/b a terminating decimal? [#permalink] New post   24 Aug 2020, 07:38
IanStewart ,

Thanks!! i got your Point.

Regards,
Rajat Chopra
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Re: If a and b are integers, is the fraction a/b a terminating decimal? [#permalink] New post   12 Sep 2020, 13:14
sjuniv32 wrote:
If \(a\) and \(b\) are integers, is the fraction \(\frac{a}{b}\) a terminating decimal?

(1) \(b\) is a prime numbers less than 7

(2) \(a\) and \(b\) are integers with no common factors other than 1.


My take will be as below:
A fraction in its lowest form will be a terminating decimal when the denominator has powers only of 2 or 5 or Both.
Also, numerator should not be a multiple of the the denominator else we will get an integer as a result and not a terminating decimal.

St1: we have no idea about numerator "a". Hence, no idea about the whether a/b is in lowest form.
Also,b is a prime number less than 7. So, b can be 2, 3, 5. To get terminating decimal, 3 should nt be in denominator.
Overall the statement is insufficient

St2: a and b have no common factor other than 1. This means a/b is in its lowest form. One criteria fulfilled.
Now , we need to know about the denominator. Oops.. no idea about deno. Hence, St2 is insufficient.

St1 + St2
a /b in lowest form --OK
We donot need to worry about the values of "a" anymore.
Denominator is either 2, 3 , 5. We donot want 3 or its power in deno but No clarity on this criteria.So, together also, the statements are insufficient.
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Re: If a and b are integers, is the fraction a/b a terminating decimal? [#permalink]
12 Sep 2020, 13:14
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Bunuel
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