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A/B is a fraction such that A and B are co-prime positive  [#permalink]

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13 00:00

Difficulty:   55% (hard)

Question Stats: 55% (01:22) correct 45% (01:28) wrong based on 293 sessions

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A/B is a fraction such that A and B are co-prime positive integers. What can be the value of B such that A/B is not a non-terminating decimal?

(A) 28
(B) 42
(C) 84
(D) 128
(E) More than two answers are correct

Originally posted by guerrero25 on 17 Jun 2013, 14:20.
Last edited by guerrero25 on 17 Jun 2013, 14:44, edited 1 time in total.
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Re: A/B is a fraction such that A and B are co-prime positive  [#permalink]

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guerrero25 wrote:
A/B is a fraction such that A and B are co-prime positive integers. What can be the value of B such that A/B is not a non-terminating decimal?

(A)28
(B)42
(C)84
(D)128
(E)More than two answers are correct

For $$\frac{A}{B}$$ to be a terminating decimal b must have the form $$2^a*5^b$$.

Every option except 128 contains a $$7$$, and since A and B do not share any factor (are co-prime) 7 will not cancel out of the denominator.

So B can only be $$128=2^7$$
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Re: A/B is a fraction such that A and B are co-prime positive  [#permalink]

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guerrero25 wrote:
A/B is a fraction such that A and B are co-prime positive integers. What can be the value of B such that A/B is not a non-terminating decimal?

(A) 28
(B) 42
(C) 84
(D) 128
(E) More than two answers are correct

A and B are co-prime means that they do not share any common factor but 1.

Thus in order A/B to be a terminating decimal B must be of the form 2^n*5^m. Only D fits.

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Math Expert V
Joined: 02 Sep 2009
Posts: 59268
Re: A/B is a fraction such that A and B are co-prime positive  [#permalink]

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4
guerrero25 wrote:
A/B is a fraction such that A and B are co-prime positive integers. What can be the value of B such that A/B is not a non-terminating decimal?

(A) 28
(B) 42
(C) 84
(D) 128
(E) More than two answers are correct

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^2$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

Questions testing this concept:
does-the-decimal-equivalent-of-p-q-where-p-and-q-are-89566.html
any-decimal-that-has-only-a-finite-number-of-nonzero-digits-101964.html
if-a-b-c-d-and-e-are-integers-and-p-2-a3-b-and-q-2-c3-d5-e-is-p-q-a-terminating-decimal-125789.html
700-question-94641.html
is-r-s2-is-a-terminating-decimal-91360.html
pl-explain-89566.html
which-of-the-following-fractions-88937.html
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Re: A/B is a fraction such that A and B are co-prime positive  [#permalink]

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Bunuel wrote:
Theory:
For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^2$$

Small correction to the above theory - should be 5^3 (not 5^2).

Thanks for the in-depth post and simple to understand explanation Bunuel!

~ Im2bz2p345 Manager  B
Joined: 10 Mar 2014
Posts: 180
Re: A/B is a fraction such that A and B are co-prime positive  [#permalink]

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Bunuel wrote:
guerrero25 wrote:
A/B is a fraction such that A and B are co-prime positive integers. What can be the value of B such that A/B is not a non-terminating decimal?

(A) 28
(B) 42
(C) 84
(D) 128
(E) More than two answers are correct

A and B are co-prime means that they do not share any common factor but 1.

Thus in order A/B to be a terminating decimal B must be of the form 2^n*5^m. Only D fits.

Hi Bunuel,

I have a doubt here question is asking A/B to be non terminating decimal here we are saying A/B to be terminating decimal it should be of form 2^n5^m pleae clarify.

Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 59268
Re: A/B is a fraction such that A and B are co-prime positive  [#permalink]

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PathFinder007 wrote:
Bunuel wrote:
guerrero25 wrote:
A/B is a fraction such that A and B are co-prime positive integers. What can be the value of B such that A/B is not a non-terminating decimal?

(A) 28
(B) 42
(C) 84
(D) 128
(E) More than two answers are correct

A and B are co-prime means that they do not share any common factor but 1.

Thus in order A/B to be a terminating decimal B must be of the form 2^n*5^m. Only D fits.

Hi Bunuel,

I have a doubt here question is asking A/B to be non terminating decimal here we are saying A/B to be terminating decimal it should be of form 2^n5^m pleae clarify.

Thanks

Please read the question carefully: what can be the value of B such that A/B is not a non-terminating decimal? So, the question asks for such value of B so that A/B will be terminating decimal.
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Re: A/B is a fraction such that A and B are co-prime positive  [#permalink]

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In simpler words, if B has only 2s and or 5s and nothing else in its prime factorization, then A/B will not be a non-terminating decimal.
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Re: A/B is a fraction such that A and B are co-prime positive  [#permalink]

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_________________ Re: A/B is a fraction such that A and B are co-prime positive   [#permalink] 13 Jun 2019, 11:20
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