Difference between revisions of "2014 AMC 10A Problems/Problem 11"
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==Solution 2 (Using The Answers)== | ==Solution 2 (Using The Answers)== | ||
− | For coupon <math>1</math> to be the most effective, we want 10% of the price to be greater than 20. This clearly occurs if the value is over 200. | + | For coupon <math>1</math> to be the most effective, we want 10% of the price to be greater than 20. This clearly occurs if the value is over 200. For coupon 1 to be more effective than coupon 3, we want to minimize the value over 200, so <math>\textbf{(C)}</math> is the smallest number over 200. |
==See Also== | ==See Also== |
Revision as of 14:03, 23 December 2016
- The following problem is from both the 2014 AMC 12A #8 and 2014 AMC 10A #11, so both problems redirect to this page.
Problem
A customer who intends to purchase an appliance has three coupons, only one of which may be used:
Coupon 1: off the listed price if the listed price is at least
Coupon 2: off the listed price if the listed price is at least
Coupon 3: 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
?
Solution 1
Let the listed price be . Since all the answer choices are above
, we can assume
. Thus the discounts after the coupons are used will be as follows:
Coupon 1:
Coupon 2:
Coupon 3:
For coupon to give a greater price reduction than the other coupons, we must have
and
.
From the first inequality, the listed price must be greater than , so answer choices
and
are eliminated.
From the second inequality, the listed price must be less than , so answer choices
and
are eliminated.
The only answer choice that remains is .
Solution 2 (Using The Answers)
For coupon to be the most effective, we want 10% of the price to be greater than 20. This clearly occurs if the value is over 200. For coupon 1 to be more effective than coupon 3, we want to minimize the value over 200, so
is the smallest number over 200.
See Also
2014 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
2014 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.