Question: Hummingbird Feeder

Comment on Hummingbird Feeder

hi brent
is there any other way to solve this question ?
gmat-admin's picture

Sorry, but I can't think of an alternate solution offhand.

how about this?

the volume decreases 1/4 every 6 hours, so the volume every 6 hours is 3/4 of the current volume.
to go back in time, I multiply by the inverse of 3/4 which is 4/3

P+12 = 81/16
P+6 = (81/16) * 4/3 = 27/4
P = (27/4) * 4/3 = 9
P-6 = (9) * 4/3 = 12
gmat-admin's picture

That definitely works - nice job!!

Hi Brent, not sure I quite understand this inverse bit and reason for it. Could you elaborate a bit more of this line? Thanks Brent

"to go back in time, I multiply by the inverse of 3/4 which is 4/3"
gmat-admin's picture

Let's say we want to solve the equation: (2/3)x = 12
If we multiply both sides by 3/2 (the reciprocal/inverse), we get: (3/2)(2/3)x = 12(3/2)
Simplify: x = 18

Does that help?

Thanks Brent. I understand your example. So in below calculation if we multiply 4/3 both sides...it seems it's back to original equation again ? Not sure which part has gone wrong? Thanks Brent

4/3 (P+6) = (81/16) * 3/4 * 4/3
4/3 (P+6) = (81/16)
(P+6) = (81/16) * 3/4
gmat-admin's picture

I think you're assuming that the letter P here represents some value.
In m4rt14n's solution above, P is the PRESENT time.
Similarly, P+6 represents 6 hours from now (i.e., present time + 6 hours)
P+12 represents 12 hours from now
And P-6 represents 6 hours ago.

Brilliant!

Hi Brent,
Instead of 6 hrs ago i started my calculation from 'now' which i got as 9 (if I compare from your table it's correct)..but then how will i proceed further to calculate for 6 hrs ago.
Please help and let me know if this approach is correct.
gmat-admin's picture

If we start at NOW, we get:

Let V = Volume NOW.

NOW: V
6 hrs from now: (3/4)V
12 hrs from now: (3/4)(3/4)V

So we get: (3/4)(3/4)V = = 81/16
Simplify: (9/16)V = 81/16
Multiply both sides by 16 to get: 9V = 81
Solve: 9
So, the present volume is 9 ounces

To find the volume 6 hours in the FUTURE, we take the present volume and MULTIPLY by 3/4.

To find the volume 6 hours in the PAST, we take the present volume and DIVIDE by 3/4.

So, volume 6 hours ago = 9 ÷ 3/4
9 ÷ 3/4 = 9 x 4/3 = 12

Answer: C

Cheers,
Brent

To avoid big numbers I converted 81/16 to 3^4/4^2 and so(3/4)^3*P = (3/4)^3 * (3/4^-1) then P=3/1/4 so P=3*4 =12
gmat-admin's picture

Very nice!!

you know what I do? I did it this way,

(3/4)x*(3/4) = 81/16, x = 9, 0.75x = 9, x = 12
gmat-admin's picture

I'm not sure what those steps mean. Do you care to elaborate?

so 3/4 is 75%, decrease 1/4 (25% every 6 hours), so let the current equal to x, x(1-0.25)(1-0.25)[decreased by 25% for two times), so current solved to be 9 ounces, then the target question asks for 6 hours ago which means (x-0.25) = 9, so x = 12
gmat-admin's picture

Perfect!

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