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Two watermelons of the same sort, A and B, are on sale.

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Manager
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Two watermelons of the same sort, A and B, are on sale. [#permalink]

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New post 25 Sep 2008, 21:25
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

1. Two watermelons of the same sort, A and B, are on sale.
Watermelon A has circumference of 60 cm, watermelon B, of 50 cm.
If the price of watermelon A is 1.5 times the price of watermelon B, which watermelon is a
better buy?

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Manager
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Re: watermelon [#permalink]

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New post 25 Sep 2008, 21:47
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To get the better buy, we need to make sure we get more volume for the price.

Watermelon A
2*pi*R1 = 60 ==> R1 = 30/pi
Volume of A = (4/3) pi (R1^3) = (4/3)*pi*((30/pi)^3) = (4/3) * 3.14 * (30/3.14)^3 = 4 * 10^3 = appr 4000

Watermelon B
2*pi*R2 = 50 ==> R2 = 25/pi
Volume of B = (4/3) pi (R2^3) = (4/3)*pi*((25/pi)^3) = 4/3 * 3.14 * (25/3.14)^3 = 4 * 8^3 = appr 2000

So if v get watermelon B for 10 dollars, we'll need to pay $20 to get 2 watermelons which will be 4000units which is equal to watermelon A.

so its always better to pay $15 to get watermelon A, since we r getting 4000units for $15.

S.

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Re: watermelon [#permalink]

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New post 26 Sep 2008, 14:04
sumanamba wrote:
To get the better buy, we need to make sure we get more volume for the price.

Watermelon A
2*pi*R1 = 60 ==> R1 = 30/pi
Volume of A = (4/3) pi (R1^3) = (4/3)*pi*((30/pi)^3) = (4/3) * 3.14 * (30/3.14)^3 = 4 * 10^3 = appr 4000

Watermelon B
2*pi*R2 = 50 ==> R2 = 25/pi
Volume of B = (4/3) pi (R2^3) = (4/3)*pi*((25/pi)^3) = 4/3 * 3.14 * (25/3.14)^3 = 4 * 8^3 = appr 2000

So if v get watermelon B for 10 dollars, we'll need to pay $20 to get 2 watermelons which will be 4000units which is equal to watermelon A.

so its always better to pay $15 to get watermelon A, since we r getting 4000units for $15.

S.


Good One. The key is to identify that circle is 2-D & sphere is circle's 3-D form.

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Re: watermelon [#permalink]

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New post 26 Sep 2008, 16:40
how do we know that the watermelons are perfect spheres?

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Re: watermelon [#permalink]

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New post 26 Sep 2008, 19:37
bigtreezl wrote:
how do we know that the watermelons are perfect spheres?


Just because we have no other information regarding shape here and we are given only the circumferences, we are forced to assume it is a sphere :)

I am not sure if this is a GMAT type question. GMAC prefers to leave no ambiguities in their questions.
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

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Re: watermelon [#permalink]

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New post 26 Sep 2008, 20:23
This is the solution i got from the gmat club test.
To determine a better buy - we need to find out which watermelon is cheaper per kilo. Watermelon with C=60 has a volume of 224,694,718 (cu. cm's?) and the watermelon with C=50 has volume of 130,031,759. C=60 watermelon is 1.7 times the size of C=50 watermelon. Therefore C=60 is obviously the better buy.

I was just wondering how they came up with the volume?

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Re: watermelon   [#permalink] 26 Sep 2008, 20:23
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Two watermelons of the same sort, A and B, are on sale.

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