2014 AMC 12A Problem 8
Attempt Problem 8 of the 2014 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
8.
A customer who intends to purchase an appliance has three coupons, only one of which may be used:
Coupon off the listed price if the listed price is at least
Coupon off the listed price if the listed price is at least
Coupon off the amount by which the listed price exceeds
For which of the following listed prices will coupon offer a greater price reduction than either coupon or coupon
Answer: C
Small hint:
Let be the listed price and write each coupon’s reduction as an expression in
Big hint:
Coupon beats coupon when and beats coupon when
Solution:
For a price the reductions are and
Coupon beats coupon when that is Coupon beats coupon when that is
The only listed price in is
Thus, the correct answer is C.
Problem 8 in other years
- 1950 AMC 12
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