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Helga and Rob like corn on cob. Each prefers to eat the gene

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Helga and Rob like corn on cob. Each prefers to eat the gene [#permalink] New post 06 Aug 2012, 04:46
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Helga and Rob like corn on the cob. Each prefers to eat the genetically modified type corn, which has perfect cylindrical shape.
Helga likes to eat her corn by chewing circular strips of equal width. Rob prefers to go along the height of the cylinder, munching straight strips of the same width as Helga's strips. If Helga eats half as many circular strips as Rob eats straight strips, what is the ratio between the height and the radius of the corn on the cob?

\((A)\, 1:2\)
\((B)\, 2:1\)
\((C)\, 1:\pi\)
\((D)\, \pi:1\)
\((E)\, 1:\sqrt{\pi}\)
[Reveal] Spoiler: OA

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Re: Helga and Rob like corn on cob. Each prefers to eat the gene [#permalink] New post 06 Aug 2012, 05:04
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EvaJager wrote:
Helga and Rob like corn on cob. Each prefers to eat the genetically modified type corn, which has perfect cylindrical shape.
Helga likes to eat her corn by chewing circular strips of equal width. Rob prefers to go along the height of the cylinder, munching straight strips of the same width as Helga's strips. If Helga eats half as many circular strips as Rob eats straight strips, what is the ratio between the height and the radius of the corn on cob?

\((A)\, 1:2\)
\((B)\, 2:1\)
\((C)\, 1:\pi\)
\((D)\, \pi:1\)
\((E)\, 1:\sqrt{\pi}\)


Say the the width of the strip each eats is \(x\).

Since Helga eats the corn circularly, then the number of strips she eats is \(\frac{h}{x}\).
Since Rob eats the corn along the height, then the number of strips he eats is \(\frac{2\pi{r}}{x}\).

We are told that \(\frac{h}{x}=\frac{1}{2}*\frac{2\pi{r}}{x}\) --> \(\frac{h}{r}=\pi\).

Answer: D.
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Re: Helga and Rob like corn on cob. Each prefers to eat the gene [#permalink] New post 17 Aug 2012, 19:55
Bunuel wrote:
EvaJager wrote:
Helga and Rob like corn on cob. Each prefers to eat the genetically modified type corn, which has perfect cylindrical shape.
Helga likes to eat her corn by chewing circular strips of equal width. Rob prefers to go along the height of the cylinder, munching straight strips of the same width as Helga's strips. If Helga eats half as many circular strips as Rob eats straight strips, what is the ratio between the height and the radius of the corn on cob?

\((A)\, 1:2\)
\((B)\, 2:1\)
\((C)\, 1:\pi\)
\((D)\, \pi:1\)
\((E)\, 1:\sqrt{\pi}\)


Say the the width of the strip each eats is \(x\).

Since Helga eats the corn circularly, then the number of strips she eats is \(\frac{h}{x}\).
Since Rob eats the corn along the height, then the number of strips he eats is \(\frac{2\pi{r}}{x}\).

We are told that \(\frac{h}{x}=\frac{1}{2}*\frac{2\pi{r}}{x}\) --> \(\frac{h}{r}=\pi\).

Answer: D.


Please explain how you obtained the number of strips eaten by each of them; how was the equality obtained? How can we use the information about the way of their eating corn to determine the number of strips eaten by each of them.
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Re: Helga and Rob like corn on cob. Each prefers to eat the gene [#permalink] New post 20 Aug 2012, 09:51
The circumference of the cylinder is 2*pi*r.
Dividing by x gives the number of vertical strips ,because each strip is of width x.
The height of the cylinder is h.Dividing by x will give you the number of horizontal strips.
Now apply the data given in the question and equate.
Hope this helps .
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Re: Helga and Rob like corn on cob. Each prefers to eat the gene [#permalink] New post 13 Nov 2014, 22:29
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Re: Helga and Rob like corn on cob. Each prefers to eat the gene   [#permalink] 13 Nov 2014, 22:29
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