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M05 #4

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leeye84
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Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   20 Aug 2007, 11:15
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 Watermelon A is 1.5 times more expensive than Watermelon B, which watermelon is a better buy? (assume watermelon is spherical in shape)

A) A
B) B
C) Either
D) Neither
E) Impossible

Please explain.



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Re: M05 #4 [#permalink] New post   24 Sep 2008, 18:26
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dczuchta wrote:
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?

(You may assume that the watermelon is spherical in shape)

Answer: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.

My questions: How do we come up with these two volumes with the equation 4/3 pie r^3. Also, what circumference equation is used to determine r in the sphere? I thought the circumference can only be determined on a 2 dimensional object and not a 3 dimensional one (sphere). Thank you.


here is what's important.

Radius of A = R_a
Radius of B = R_b

R_a/R_b = circumference of A/circumference of B = 6/5
Therefore the ratio of volumes of A and B is 6^3/5^3

Price of A/Price of B should be 6^3/5^3 if they are priced fairly
Since actual Price of A/Price of B = 1.5 < 1.7 < 6^3/5^3 -> A is a better buy
I hope that helps.
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M05 #4 [#permalink] New post   24 Sep 2008, 10:57
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Two watermelons, \(A\) and \(B\) , are on sale. Watermelon \(A\) has a circumference of 6 inches; watermelon \(B\) , 5 inches. If the price of watermelon \(A\) is 1.5 times the price of watermelon \(B\) , which watermelon is a better buy?

(Assume that the two watermelons are spheres).

(A) A
(B) B
(C) Neither
(D) Both
(E) Impossible to determine

Show SpoilerOA
A

Source: GMAT Club Tests - hardest GMAT questions

Answer: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.

My questions: How do we come up with these two volumes with the equation 4/3 pie r^3. Also, what circumference equation is used to determine r in the sphere? I thought the circumference can only be determined on a 2 dimensional object and not a 3 dimensional one (sphere). Thank you.

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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] 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: Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   30 Oct 2008, 08:02
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I think A is the best buy as the volume of the watermelon is important.
The volume is 4/3pi*r^3
so the radius of watermelon A= 30/pi
watermelon B=25/pi
So keeping the 4/3 and pi constant the ratio of volume is 30*30*30/25*25*25=1.7
But the price of A is 1.5 times of B where as the volume of A is 1.7 times of B.
So I think A is the best buy

What is the OA??
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Re: M05 #4 [#permalink] New post   30 Apr 2011, 17:32
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Here's how I solved it even though I couldn't fully recall the formula for calculating volume of a sphere; all I remembered is that it has an r^3 in it.

Radius of first = 6/2pi
Radius of first = 5/2pi

Taking a ratio of these two -
6/5
Cube - 216/125, which is more than 1.5 times
So a 1.5 times increase in cost gives more watermelon /dollar.

Ans - A.
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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   20 Aug 2007, 11:45
leeye84 wrote:
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 Watermelon A is 1.5 times more expensive than Watermelon B, which watermelon is a better buy? (assume watermelon is spherical in shape)

A) A
B) B
C) Either
D) Neither
E) Impossible

Please explain.


A is better

PriceA / Price B = 1.5
If you find the ratio of volume to be greater, then it is a better buy.
Volume of Sphere = (4/3) * P * R^3
Va / Vb = (Ra / Rb)^3

Ra = 60 / (2*P) = 30 / P
Rb = 50 / (2*P) = 25 / P

Va / Vb = (30/25)^3 = (1.2)^3 = 1.728
A is a better buy.
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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   20 Aug 2007, 21:08
My answer is A - the same method as bkk145, but this is exactly the question where I think too much - what about density, weight, taste? We cannot make a decision based only on volume =)
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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   21 Aug 2007, 21:15
bkk145 wrote:
leeye84 wrote:
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 Watermelon A is 1.5 times more expensive than Watermelon B, which watermelon is a better buy? (assume watermelon is spherical in shape)

A) A
B) B
C) Either
D) Neither
E) Impossible

Please explain.


A is better

PriceA / Price B = 1.5
If you find the ratio of volume to be greater, then it is a better buy.
Volume of Sphere = (4/3) * P * R^3
Va / Vb = (Ra / Rb)^3

Ra = 60 / (2*P) = 30 / P
Rb = 50 / (2*P) = 25 / P

Va / Vb = (30/25)^3 = (1.2)^3 = 1.728
A is a better buy.


fantastic explaination. I wish every answer is posted with as much detail as your answer.
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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   22 Aug 2007, 01:48
Pretty easy question

calculate volumes

have to know

circumference = 2*pi*diameter

diamter = 2*radius

volume of sphere = 4/3 * pi * radius^3

then assume A costs 1.5, and B costs 1

then see how many cubic centimeters you get per dollar........... with A you get 304, with B you get ~264

A is the better buy



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Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   25 Sep 2008, 21:25
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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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] 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: Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   26 Sep 2008, 16:40
how do we know that the watermelons are perfect spheres?
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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] 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.
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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] 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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Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   30 Oct 2008, 06:15
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?

(You may assume that the watermelon is spherical in shape)


* A
* B
* Either
* Neither
* Impossible to determine



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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   30 Oct 2008, 07:31
It's B.

I look at it as a dimension/price ratio: 60:1,5 for watermelon A, 50:1 watermelon B. Thus, watermelon B worths more than A.

Right?
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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   30 Oct 2008, 08:30
subarao wrote:
I think A is the best buy as the volume of the watermelon is important.
The volume is 4/3pi*r^3
so the radius of watermelon A= 30/pi
watermelon B=25/pi
So keeping the 4/3 and pi constant the ratio of volume is 30*30*30/25*25*25=1.7
But the price of A is 1.5 times of B where as the volume of A is 1.7 times of B.
So I think A is the best buy

What is the OA??



Definitely we need to consider weight not area or redius/diameter or circumference.
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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   30 Oct 2008, 11:09
Will it be considered that the watermelon with greater volume will be of greater weight? (well, then we have to assume the densities of the both watermelon are same).
If not then, the condition is not sufficient enough.
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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink] New post   30 Oct 2008, 11:10
so it is impossible to determine from the above information. Am I right GMAT tiger?
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Re: Two watermelons of the same sort, A and B, are on sale. [#permalink]
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