It costs $2,250 to fill right circular cylindrical Tank R with a certa

Directly proportional means

Volume = k * Price
Volume = k * 2250

We know that Volume =\( \pi*r^2*h \) so price is directly proportional to square of the radius (if height is constant). If the radius doubles, the price becomes 4 times. If radius becomes half, price becomes 1/4th. So you can get the actual price if you know that height doesn't change.

Check this post for some more examples:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2013/0 ... -directly/

The volume of a cylinder = \(πr^2h\)

From S1:

\(D_R = 2D_S\)
But, no info about height.
Hence, Insufficient.

From S2:

\(H_R = H_S\)
But, no info about radius.
Hence, Insufficient.

Combining both:
We can find the Radius and height.
Sufficient.

C is the answer.

since volume is directly proportional to cost of chemical and volume is piDH so u need both to find the ans.hence C

tank r cost = 2250 $ is same as the vol of tank - 2250 ; pi * r^2 *h = 2250
now for tank S we need its r and h values
#1
Dr= 2Ds
not sufficient as h is missing radius of s = radius of R /4
#2
h is same , r is missing
from 1 & 2
pi* r2*h /4 = 2250/4 ; 562.5$
IMO C

Hello experts, chetan2u VeritasKarishma GMATBusters
I was wondering whether could someone explain this part ""If the cost to fill any tank with this chemical is directly proportional to the volume of the chemical needed to fill the tank""

From what I know the formula when two elements a and b are directly proportional is a=kb , so I was wondering what is the impact of this phrase in this question , is it to just state that the πr^2h=2250 or if we were to strictly follow the information given we would have to present it with some other way like πr^2h=k2250 ...

""If the cost to fill any tank with this chemical is directly proportional to the volume of the chemical needed to fill the tank"" translates to πr^2h=k2250 :

Volume of a cylinder = \(πr^2h\)

(1) We are not given \(h\); Insufficient.

(2) We are given \(r\); Insufficient


Considering both:
We have both \(r & h\); Sufficient.

The answer is \(C\)

KarishmaB



We have ratio information, but no count. We don't know what h equals. We don't know what r equals. It's not possible to solve for two variables in one equation. How can you solve it?

kaylaquijas

We are given that price is directly proportional to volume.

Price = k*Volume

2250 = k * Vr
(Vr is the volume of tank R)

We need the cost to fill tank S. If we can find the relation between the volume of tank R and volume of tank S, we can find the price of filling tank S. Say their volumes are same. Then tank S will also need $2250 to fill up. Say volume of tank S is twice the volume of tank R, then tank S will need $4500 to fill up and so on...


Volume of a tank R = pi*r^2*h (it depends on radius and height)

(1) The diameter of the interior of Tank R is twice the diameter of the interior of Tank S.
So tank S has half the diameter of tank R i.e. it has half the radius of tank R.
This means that the volume of tank S is one fourth the volume of tank R if their heights are the same. Else volume will depend on height too.
Not sufficient alone since we don't know the relation of their heights.


(2) The interiors of Tanks R and S have the same height.
Now we know that their heights are the same. But alone this is not sufficient because we don't have the relation of their radii.

Using both, we know that radius of S is 1/2 of the radius of tank R and height of tank S is the same as the height of tank R.

Volume of tank S = pi*r^2*h/4

Since the volume of tank S is only 1/4th of volume of tank R, price of filling it up will also be 1/4th of $2250 = $562.5

Though we don't need to do all these calculations.

KarishmaB
Thank you for this helpful explanation. To clarify, on the formula "Price = k*Volume" can you have Price*k = Volume instead?

I just didn't know if I multiple the constant by price or formula in setting up the problem to solve. Thank you again

It doesn't matter how you set it up.

Price = k * Volume or Volume = k * Price

The value of k in the two cases will be different. For example, we may find that Price = 3 * Volume, but had we set it up the other way around, we may have found that Volume = (1/3)* Price
Both are the same. k = 3 in one case and k = 1/3 in the other case.

dear Bunuel
I picked up E , I wonder how we know the chemical is filled fully in the right circular cylindrical tank.

It costs $2,250 to fill right circular cylindrical Tank R with a certain industrial chemical, means it costs that much to fill the cylinder up to its capacity. Otherwise the sentence won't make sense.
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