2019 AMC 8 Problem 14
Attempt Problem 14 of the 2019 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2019 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
14.
Isabella has coupons that can be redeemed for free ice cream cones at Pete’s Sweet Treats. In order to make the coupons last, she decides that she will redeem one every days until she has used them all. She knows that Pete’s is closed on Sundays, but as she circles the dates on her calendar, she realizes that no circled date falls on a Sunday. On what day of the week does Isabella redeem her first coupon?
Monday
Tuesday
Wednesday
Thursday
Friday
Answer: C
Small hint:
Every days advances the weekday by
Big hint:
The six days hit every weekday except one
Video solution:
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Written solution:
Let us go through the answer choices.
Each redemption is days later, which advances the weekday by days.
Starting on day the six redemption days are and modulo
The only missed weekday is so Sunday must be four days after the first redemption day. Four days before Sunday is Wednesday.
Thus, the correct answer is C.
Problem 14 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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- 1998 AMC 8
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