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# If m and n are integers, what is the smallest possible value

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Director
Joined: 07 Jan 2018
Posts: 598
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Kudos [?]: 538 [1] , given: 88

If m and n are integers, what is the smallest possible value [#permalink]  22 May 2018, 08:36
1
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Question Stats:

87% (01:06) correct 12% (00:59) wrong based on 8 sessions
If m and n are integers, what is the smallest possible value of integer m, if m/n = 0.36363636..........?

[Reveal] Spoiler:
4

src: orbit test prep
Director
Joined: 07 Jan 2018
Posts: 598
Followers: 7

Kudos [?]: 538 [3] , given: 88

Re: If m and n are integers, what is the smallest possible value [#permalink]  24 May 2018, 21:57
3
KUDOS
Since the digits after decimal point is repeating in a pair of 36 when we multiply $$\frac{m}{n}$$ by 100 we get 36.363636.....

Therefore, $$100 * \frac{m}{n}- \frac{m}{n} = 36$$
or, $$99 \frac{m}{n} = 36$$
or, $$99m = 36n$$
The ans requires the value of m such that m/n is reduced to its lowest fraction
Therefore when dividing both sides by 9 we get,
$$11m = 4n$$
or, $$\frac{m}{n}$$ = $$\frac{4}{11}$$
Hence, m = 4
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Re: If m and n are integers, what is the smallest possible value   [#permalink] 24 May 2018, 21:57
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