A farmer determines that the price P per pound of a certain seasonal

Question

A farmer determines that the price P per pound of a certain seasonal product and the number S of pounds of this product sold per month are related by the formula \(P = \frac{K}{\sqrt{S}}\) where S > 0 and K is a constant. If S decreases by 75 percent, then by what percent does the price P increase, according to this formula?

A. 150%
B. 100%
C. 75%
D. 50%
E. 25%

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Official Answer

B

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Bunuel · Accepted Answer

We are given that for some constant K, K = P\sqrt{S} . If S' becomes S/4, which corresponds to a decrease of 75%, then \sqrt{S'}=\sqrt{\frac{S}{4}}=\frac{\sqrt{S}}{2} . To maintain the same constant K, P' must become 2P, which corresponds to a 100% increase. Answer: B. GMAT-Club-Forum-6xgvc7jd.png

Dhrm · Answer

Q. A farmer determines that the price P per pound of a certain seasonal product and the number S of pounds of this product sold per month are related by the formula P=KS√𝑃=𝐾𝑆 where S > 0 and K is a constant. If S decreases by 75 percent, then by what percent does the price P increase, according to this formula?

Sol: Assumed K as 32 and S as 16 (as it will be easier to calculate)

P= k/√s
= 32/√16
= 32/4
=8

Now let's decrease S by 75%, which will be 16*1/4=4 and keep the K contsant as 32.

P= 32/√4
= 32/2
= 16

So the resulting value of P increased from 8 to 16, an increase of 100%. Ans. choice B.

Bunuel · Answer

Can you please post a screenshot? Thank you!

Fish181 · Answer

Thanks!! https://gmatclub.com/forum/download/file.php?id=82200 GMAT-Club-Forum-dam84ct4.png

Bunuel · Answer

_______________________ Formatted the question. Thank you! GMAT-Club-Forum-hvk0txmg.png

DanTheGMATMan · Answer

Similar to a direct or inverse proportion. Can solve it using the variables but it's easier just to choose numbers for p and s to get a constant K and then reduce s as they say and then resolve for P:

https://www.youtube.com/watch?v=wRwL_-OvMw4

ronnnie · Answer

Let , P = 10, S = 100 . hence , placing them in the given formula : K = 100.
Now , S reduced by 75% hence, new S = 25, and K (we found) = 100.
Gives us ,

P = 20. and thats 100% increase. answer.

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A farmer determines that the price P per pound of a certain seasonal

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