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# Dividing 207 by 1.15

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Intern
Joined: 09 Sep 2017
Posts: 10

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09 Sep 2017, 06:22
My brain must be fried, but I cannot seem to find a simple way to do this. Is it possible without long division, is there some shortcut/trick I am missing?

It's one of the OG questions, any help is very much appreciated.
Director
Joined: 21 May 2013
Posts: 656
Re: Dividing 207 by 1.15  [#permalink]

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09 Sep 2017, 06:36
nacho93 wrote:
My brain must be fried, but I cannot seem to find a simple way to do this. Is it possible without long division, is there some shortcut/trick I am missing?

It's one of the OG questions, any help is very much appreciated.

1.Multiply both numerator and denominator by 100 to remove the decimals
2. Fraction becomes (20700/115)
3. Now, when you try to divide denominator by 5, you would easily know that 115 =5*23. See if 207 is also divisible by 23. Yes! It is!
4. 23*9=207 and 23*5=115. It should be easy after that.
Math Expert
Joined: 02 Sep 2009
Posts: 54371
Re: Dividing 207 by 1.15  [#permalink]

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09 Sep 2017, 08:00
nacho93 wrote:
My brain must be fried, but I cannot seem to find a simple way to do this. Is it possible without long division, is there some shortcut/trick I am missing?

It's one of the OG questions, any help is very much appreciated.

That question is discussed here: https://gmatclub.com/forum/the-price-of ... 31794.html

Transform decimal into fraction: $$1.15=1\frac{15}{100}=1\frac{3}{20}=\frac{23}{20}$$.

$$Bill*1.15=207$$ --> $$Bill*\frac{23}{20}=207$$ --> $$Bill*\frac{23}{20}=9*23$$ --> $$\frac{Bill}{20}=9$$ --> $$Bill=180$$.

Hope it helps.
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Intern
Joined: 09 Sep 2017
Posts: 10
Re: Dividing 207 by 1.15  [#permalink]

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09 Sep 2017, 14:08
Bunuel wrote:
nacho93 wrote:
My brain must be fried, but I cannot seem to find a simple way to do this. Is it possible without long division, is there some shortcut/trick I am missing?

It's one of the OG questions, any help is very much appreciated.

Transform decimal into fraction: $$1.15=1\frac{15}{100}=1\frac{3}{20}=\frac{23}{20}$$.

$$Bill*1.15=207$$ --> $$Bill*\frac{23}{20}=207$$ --> $$Bill*\frac{23}{20}=9*23$$ --> $$\frac{Bill}{20}=9$$ --> $$Bill=180$$.

Hope it helps.

Thank you so much, exactly what I was looking for!
Re: Dividing 207 by 1.15   [#permalink] 09 Sep 2017, 14:08
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