Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2014 AMC 8 Problems/Problem 23"

m (→‎Video Solution)
m (→‎Solution)
Line 19: Line 19:
 
https://youtu.be/6xNkyDgIhEE?t=735
 
https://youtu.be/6xNkyDgIhEE?t=735
  
−
==Solution==
+
==Video Solution==
−
The maximum amount of days any given month can have is <math>31</math>, and the smallest two digit primes are <math>11, 13,</math> and <math>17</math>. There are a few different sums that can be deduced from the following numbers, which are <math>24, 30,</math> and <math>28</math>, all of which represent the three days.  Therefore, since Brittany says that the other two people's uniform numbers are earlier, so that means Caitlin and Ashley's numbers must add up to <math>24</math>.  Similarly, Caitlin says that the other two people's uniform numbers is later, so the sum must add up to <math>30</math>.  This leaves <math>28</math> as today's date.  From this, Caitlin was referring to the uniform wearers <math>13</math> and <math>17</math>, telling us that her number is <math>11</math>, giving our solution as <math>\boxed{(A)=11}</math>.
+
https://youtu.be/6xNkyDgIhEE?t=735
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2014|num-b=22|num-a=24}}
 
{{AMC8 box|year=2014|num-b=22|num-a=24}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 20:15, 6 October 2020

Problem

Three members of the Euclid Middle School girls' softball team had the following conversation.

Ashley: I just realized that our uniform numbers are all $2$-digit primes.

Brittany : And the sum of your two uniform numbers is the date of my birthday earlier this month.

Caitlin: That's funny. The sum of your two uniform numbers is the date of my birthday later this month.

Ashley: And the sum of your two uniform numbers is today's date.

What number does Caitlin wear?

$\textbf{(A) }11\qquad\textbf{(B) }13\qquad\textbf{(C) }17\qquad\textbf{(D) }19\qquad \textbf{(E) }23$

Solution 1

The maximum amount of days any given month can have is $31$, and the smallest two digit primes are $11, 13,$ and $17$. There are a few different sums that can be deduced from the following numbers, which are $24, 30,$ and $28$, all of which represent the three days. Therefore, since Brittany says that the other two people's uniform numbers are earlier, so that means Caitlin and Ashley's numbers must add up to $24$. Similarly, Caitlin says that the other two people's uniform numbers is later, so the sum must add up to $30$. This leaves $28$ as today's date. From this, Caitlin was referring to the uniform wearers $13$ and $17$, telling us that her number is $11$, giving our solution as $\boxed{(A)=11}$.

https://youtu.be/6xNkyDgIhEE?t=735

Video Solution

https://youtu.be/6xNkyDgIhEE?t=735

See Also

2014 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 22 		Followed by
Problem 24
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 AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2014_AMC_8_Problems/Problem_23&oldid=134731"