DH99 wrote:

DH99 wrote:

The price of a pastry when made fresh was $P.Each hour after the first hour the price decreased by 20%.If Lampard bought the pastry when it was just made whereas his sister bought the pastry after 3 hours, then the price paid by Lampard’s sister was what percent less than that paid by Julie?

A. 33.33%

B. 40%

C. 44%

D. 48.8%

E. 51.2 %

genxer123 wrote:

Pastry price decreases by 20 percent for each hour after it is made. Call initial price P. Decrease of 20 percent = 1 - .20 = .80

Fresh out of oven = P

1 hour later = .80P

2 hours later = .64P (.80P * .80)

3 hours later = .512P (.64P * .80)

Lampard bought a pastry fresh and paid P.

His sister bought a pastry three hours later. She paid .512P

Price paid by Lampard’s sister was what percent less than that paid by Lampard?

Percent change = \(\frac{change}{original}\) * 100

Change is P - .512P = .488P

\(\frac{.488P}{1P}\) = .488 * 100, or

48.8% less

Answer D

DH99 wrote:

Hi,

genxer123: It's given Each hour after the first hour the price decreased by 20%.So, why it will not be: Say when we take p=100.

Fresh out of oven = P =100

1 hour later = 100 (same since Each hour after the first hour)

2 hours later = 80

3 hours later = 64

DH99 , good question. I agree that the highlighted phrase is confusing.

After plugging in numbers as you did, the "percent less than" was \(\frac{(100 - 64)}{100}\) * 100 = 36 percent less.

That's not an option in the answer choices. Conclusion: I was wrong to think, "One hour passed, and AFTER THAT, the price decreased every hour, so first decrease hits at the end of the second hour."

So I thought about

when "after the first hour" could begin to toll. When does "the first hour" start and end?

Say that out of the oven time is 0:00. Clock begins to run. 60 minutes pass = one hour.

Now we are at 1:00. Think of a round clock face, put one tick mark at 0:00, and another at 1:00.

At the end of that one hour, we are "at" the tick mark that signals the end of the first hour; at 1:00 we are, time wise, at "after the first hour. . ." and "the price decrease[s] by 20%."

The confusion comes from "each" at the beginning of the sentence.

"Each hour after the first hour" seems to suggest that the first hour is not in the group of hours where a decrease happens. The first hour IS in that group.

If I were editing for clarity, I would rewrite: "For every hour after the pastry is taken fresh from the oven, the price decreased by 20 percent."

That said, although I dislike the phrase thoroughly, its obscure quality nonetheless has a meaning that is defensible. Barely, but defensible.

If the answer choices

had contained 36 percent, I'd argue otherwise.

Does that help? If not, keep asking about what you don't understand.

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"