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# GMAT Diagnostic Test Question 8

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Re: GMAT Diagnostic Test Question 8 [#permalink]

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01 Mar 2010, 18:00
A good way to approach this type of problems is knowing that:

XY/99= 0.XYXYXY

In this case we have that m/n=0.3636 --> we now that n has to be 99.. hence m=36.

36/99=(9*4)/(9*11) --> 4/11 then m=4!
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Re: GMAT Diagnostic Test Question 8 [#permalink]

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04 May 2010, 15:20
So is there a way to get 0.99999999~?
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Re: GMAT Diagnostic Test Question 8 [#permalink]

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05 May 2010, 02:22
I'm not sure if there is a simple way to obtain 0.99999999(9). $$\frac{9}{9}$$ should result in 0.9999(9), but $$\frac{9}{9}$$ = 1.
Can any gurus answer this?
thanatoz wrote:
So is there a way to get 0.99999999~?

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Re: GMAT Diagnostic Test Question 8 [#permalink]

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05 May 2010, 03:08
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Expert's post
dzyubam wrote:
I'm not sure if there is a simple way to obtain 0.99999999(9). $$\frac{9}{9}$$ should result in 0.9999(9), but $$\frac{9}{9}$$ = 1.
Can any gurus answer this?
thanatoz wrote:
So is there a way to get 0.99999999~?

Note: it's not tested on GMAT.

$$0.(9)=1$$ - long known mathematical equality.

Proof: $$1=3*\frac{1}{3}=3*0.(3)=0.(9)$$.
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Re: GMAT Diagnostic Test Question 8 [#permalink]

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18 Oct 2010, 05:18
another easy way to solve this problem and problems of this nature

0.36363636....

so the 36 part is repeating after the decimal

suppose x = 0.36363636 ....
so 100X = 36. 36363636 ....
now why did I take 100 ? because I wanted to get a string of the repeating part before the decimal

so
99 X = 36
or X = 4/11
hence m = 4
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Re: GMAT Diagnostic Test Question 8 [#permalink]

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19 Dec 2010, 07:19
sarodearun wrote:
This is a easier way......

consider m/n = x.

x= .36(bar)
100x = 36.36(bar)

100x-x = 36.

i.e., 99x=36

x=4/11.

The original solution is great, but if you do forget the trick, I would go with this solution for sure.
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Re: GMAT Diagnostic Test Question 8 [#permalink]

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10 Sep 2011, 00:55
m=(0.36363636...)n
100m=(36.36363636...)n

100m-m = 36n
99m=36n -> 11m=4n

thus the smallest value of m is 4

Correct me if my approach is wrong
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Re: GMAT Diagnostic Test Question 8 [#permalink]

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14 Sep 2011, 23:37
dzyubam wrote:
Explanation:
 Rating:

We are dealing with a repeating decimal in this question. It's helpful to know that there's a way to write these kinds of decimals as a fraction. For example, the repeating decimal 0.444444444(4) may be written as $$\frac{4}{9}$$. So, $$\frac{5}{9}$$, $$\frac{7}{9}$$ and $$\frac{8}{9}$$ will all be repeating decimals. You might check it in your calculator. In order to make two decimal points repeat, you have to divide the two digit number by 99. For example, $$\frac{23}{99} = 0.232323232323(23)$$. Similarly, $$\frac{36}{99} = \frac{4}{11} = 0.36363636(36)$$. Now it's clear that the minimum value of $$m = 4$$.

Perfect! I didn't know that
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Re: GMAT Diagnostic Test Question 8 [#permalink]

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28 Oct 2011, 22:54
Ans is B

m=0.363636... n
100m =36.3636... n

so 99m=36n => 11m=4n

so m=>4
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Re: GMAT Diagnostic Test Question 8 [#permalink]

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30 Oct 2011, 04:36
can i sum up lke this?
when singularly repeated(.44444..) some number is divided by 9, if two digit repeated(.363636...) then by 99?
same goes for 11 then?
got the answer correct by picking up but couldnt get your method
Re: GMAT Diagnostic Test Question 8   [#permalink] 30 Oct 2011, 04:36

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# GMAT Diagnostic Test Question 8

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