Bunuel
Each day after today, the price of gas, in cents per gallon, increases 5 cents per day. The day after the price reaches twice its current level, the price falls by 25% but then continues the pattern of increasing 5 cents per day. How much does a gallon of gas cost, in cents, at the end of 25 days, if the price today is 95 cents a gallon?
A. 165
B. 167.5
C. 170
D. 172.5
E. 175
I think this one comes down to tracking on days very carefully. It's day 21 that reboots the "plus 5 cents a day" cycle. And there are FIVE days, inclusive, between days 21 and 25.
Today = Day 0 = 95 cents
Tomorrow =
Day 1 = +5 = 100 cents
Day 2 = +5 = 105 cents
.
.
Day 19 = +5 = 190 cents
(Or, we need 95 to double, i.e., we need TWO 95s. How many days to get another 95? 95/5 = 19.)
Day 20=75% of 190 = 142.5 cents
Day 21 = +5 cents
Day 22 = +5 cents
Day 23 = +5 cents
Day 24 = +5 cents
Day 25 = +5 cents
Total added Days 21-25: 25 cents
142.5 + 25 = 167.5 cents
Thought it would take forever. Shocked myself
to discover that this brute force instance took 2:26.
Answer B.