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M05 #4

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M05 #4 [#permalink] New post 24 Sep 2008, 09:57
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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

[Reveal] Spoiler: OA
A

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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: M05 #4 [#permalink] New post 24 Sep 2008, 17:26
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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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Re: M05 #4 [#permalink] New post 30 Apr 2011, 16:32
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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: M05 #4 [#permalink] New post 06 Sep 2009, 03:46
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
B
Neither
Both
Impossible to determine

My solution:
Radius of A=3/pi
Radius of B=5/2pi
Cost of B=x$
Cost of A=1.5x=3x/2

For B,x$ can get us a watermelon with a radius of 5/2pi
For A,3x/2$.....................................................3/pi
= x$..............................................................2/pi

Comparing,2/pi with 5/2pi we see the latter is larger.Therefore for x dollars B gives us a larger value,hence B.

Please show where i went wrong.
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Re: M05 #4 [#permalink] New post 16 Nov 2010, 06:00
isn't it weird to say circumference of a sphere..??..They could have used a more appropriate term like surface area to give the hint of radius.
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Re: M05 #4 [#permalink] New post 16 Nov 2010, 08:21
Hi, Could anybody please provide the correct explaination for the above problem?
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Re: M05 #4 [#permalink] New post 16 Nov 2010, 08:44
I did it a bit different:
Ar = 3 --> Aa = 9pie
Br = 2.5 -- Ba = 6.25pie

Price per size(A) = 1.5p/9 === P/6 (remove the Pie)
Price per size(B) = p/6.25 === a little bit more than p/6 (4p/25)
means - the price per size of B is a bit higher than A...

Hope its clear...
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Re: M05 #4 [#permalink] New post 16 Nov 2010, 08:45
I think it was a good question. Thanks for the effort. +1 from me.
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Re: M05 #4 [#permalink] New post 16 Nov 2010, 09:02
True enough, the question does not sound properly worded, but we gotta do with whatever little we have been given.
Lets assume that the circumference is that of the circular cross sections of the two melons respectively.

Volume of melon A: (4/3)*pi*(6/2pi)^3 = 36/pi^2
Volume of melon B: (4/3)*pi*(5/2pi)^3 = 125/6pi^2

Say price of B is X and price of A is 3X/2.

Price of A per unit Volume: (36/pi^2)/(3X/2) = 24/Xpi^2 = 144/6Xpi^2
Price of B per unit Volume: (125/6pi^2)/X = 125/6Xpi^2

B is cheaper per unit volume. B
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Re: M05 #4 [#permalink] New post 16 Nov 2010, 09:16
Hey, thnx 144144...Bt I understood this way
As it is a sphere: A=4pr^2;A=6;B=5
Price is directly proportional to Volume, 4/3Pr3
so The ratio is 6r/3:5r/3 which 2:1.7 , and it is charged 1.5times for this difference, which means B is a better buy
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Re: M05 #4 [#permalink] New post 16 Nov 2010, 16:26
vaibhavtripathi wrote:
True enough, the question does not sound properly worded, but we gotta do with whatever little we have been given.
Lets assume that the circumference is that of the circular cross sections of the two melons respectively.

Volume of melon A: (4/3)*pi*(6/2pi)^3 = 36/pi^2
Volume of melon B: (4/3)*pi*(5/2pi)^3 = 125/6pi^2

Say price of B is X and price of A is 3X/2.

Price of A per unit Volume: (36/pi^2)/(3X/2) = 24/Xpi^2 = 144/6Xpi^2
Price of B per unit Volume: (125/6pi^2)/X = 125/6Xpi^2

B is cheaper per unit volume. B
my choice is B.

however, i don't think it is reasonable to determine the BEST BUY by only the measure of watermelon's radius. how about other more sound variables, such as sweetness, density, thickness of the skin even if A and B are from the same farm, and of the same breed...?
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Re: M05 #4 [#permalink] New post 16 Nov 2010, 22:12
my choice is E.
as per the wording of problem,
we can't find any relation between Circumference of Sphere and its Volume.
if the word would have surface area or diameter, then it would have been a diff question.
but as per the word, i would choose E.


if any1 has better explanation, please do reply.
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Re: M05 #4 [#permalink] New post 17 Nov 2010, 03:30
A.
Ra = 3/pi Rb = 5/2pi
vol a= 36/pi^2. Vol b = 21/pi^2

if we use 1.5 times the money to buy B we will get 1.5*21/pi^2 = 31.5/pi^2 which is less vol than A for the same money

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Re: M05 #4 [#permalink] New post 17 Nov 2010, 09:09
OA anybody? My answer is B.

Take the area of both A (9) and B (6.25) and divide by 1.5x and x respectively (with x being any number). B is always better buy.
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Re: M05 #4 [#permalink] New post 22 Nov 2010, 00:41
dczuchta wrote:
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

[Reveal] Spoiler: OA
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.



A

both are spherical. circumference is given => radius can be calculated => volume

4/3 pi r^3

for A:
4/3 pi (6/2.pi)^3
= 36/pi^2

for B:
4/3 pi (5/2.pi)^3
= 125/6.pi^2
= ~20.85/pi^2

ignore pi in both results. 1.5 * 20.85 = ~31-32

31-32 < 36

hence although you pay 1.5 times the price of B for A, you are getting bigger volume => less cost per unit weight.
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Re: M05 #4 [#permalink] New post 22 Nov 2010, 06:09
For A we have Ra=3/Pi
Rb=5/(2Pi)

A:
3/Pi=3*x/2
x=2/Pi

B:
5/(2*Pi)=x

Now we see that in case B we receive more for x dollars.
(B)
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Re: M05 #4 [#permalink] New post 23 Nov 2010, 09:45
:problem: :yikes
:(
wrong again
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Re: M05 #4 [#permalink] New post 03 Dec 2010, 14:03
321kumarsushant wrote:
my choice is E.
as per the wording of problem,
we can't find any relation between Circumference of Sphere and its Volume.
if the word would have surface area or diameter, then it would have been a diff question.
but as per the word, i would choose E.


if any1 has better explanation, please do reply.


I'm still not clear on this problem but the circumference will give you the radius or the diameter that you are looking for. Watermelon A has a circumference of 6. That means we can use the circumference formula to find the radius.

2(pi)r=6
r=3(pi)

You can do this for Watermelon B as well. Once we have the radius we can put it in the volume formula which is (4/3)(pi)(r^3)
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Re: M05 #4 [#permalink] New post 19 Nov 2011, 20:48
Initially,i couldn't find the approach to the question.
Good one.

+1 for A.
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Re: M05 #4 [#permalink] New post 20 Nov 2011, 12:07
radius A= 3/pi
radius B= 5/2pi
Volume A= (4/3)pi(3/pi)^3= 36/pi^2
Volume B= (4/3)pi(5/2pi)^3 = 20.8/pi^2

Price A = 1.5 Price B
Rate A*volume A = 1.5*Rate B*volume B
(36/pi^2)*Rate A = (31.2/pi^2)*Rate B

1.15 Rate A= Rate B ...Therefore Watermelon A is a better buy.
Re: M05 #4   [#permalink] 20 Nov 2011, 12:07
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