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M05 #4

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M05 #4 [#permalink]  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

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: M05 #4 [#permalink]  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.

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]  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:
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]  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]  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]  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]  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]  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]  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]  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]  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.

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Re: M05 #4 [#permalink]  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]  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]  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]  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]  23 Nov 2010, 09:45

wrong again
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Re: M05 #4 [#permalink]  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.

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]  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.

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]  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]  20 Nov 2011, 12:07
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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