Difference between revisions of "2015 AMC 10B Problems/Problem 4"

(Solution)
m (Problem 4)
Line 3: Line 3:
 
Four siblings ordered an extra large pizza. Alex ate <math>\frac15</math>, Beth <math>\frac13</math>, and Cyril <math>\frac14</math> of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of pizza they consumed?
 
Four siblings ordered an extra large pizza. Alex ate <math>\frac15</math>, Beth <math>\frac13</math>, and Cyril <math>\frac14</math> of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of pizza they consumed?
  
<math>\textbf{(A) } \text{Alex, Beth, Cyril, Dan}</math>
+
<math>\textbf{(A) } \text{Alex, Beth, Cyril, Dan}</math> <br>
<math>\textbf{(B) } \text{Beth, Cyril, Alex, Dan}</math>
+
<math>\textbf{(B) } \text{Beth, Cyril, Alex, Dan}</math> <br>
 
+
<math>\textbf{(C) } \text{Beth, Cyril, Dan, Alex}</math> <br>
<math>\textbf{(C) } \text{Beth, Cyril, Dan, Alex}</math>
+
<math>\textbf{(D) } \text{Beth, Dan, Cyril, Alex}</math> <br>
<math>\textbf{(D) } \text{Beth, Dan, Cyril, Alex}</math>
+
<math>\textbf{(E) } \text{Dan, Beth, Cyril, Alex}</math> <br>
 
 
<math>\textbf{(E) } \text{Dan, Beth, Cyril, Alex}</math>
 
  
 
==Solution==
 
==Solution==

Revision as of 16:31, 2 May 2020

Problem 4

Four siblings ordered an extra large pizza. Alex ate $\frac15$, Beth $\frac13$, and Cyril $\frac14$ of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of pizza they consumed?

$\textbf{(A) } \text{Alex, Beth, Cyril, Dan}$
$\textbf{(B) } \text{Beth, Cyril, Alex, Dan}$
$\textbf{(C) } \text{Beth, Cyril, Dan, Alex}$
$\textbf{(D) } \text{Beth, Dan, Cyril, Alex}$
$\textbf{(E) } \text{Dan, Beth, Cyril, Alex}$

Solution

Let the pizza have $60$ slices, since the least common multiple of $(5,3,4)=60$. Therefore, Alex ate $\frac{1}{5}\times60=12$ slices, Beth ate $\frac{1}{3}\times60=20$ slices, and Cyril ate $\frac{1}{4}\times60=15$ slices. Dan must have eaten $60-(12+20+15)=13$ slices. In decreasing order, we see the answer is $\boxed{\textbf{(C) }\text{Beth, Cyril, Dan, Alex}}$.

See Also

2015 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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

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

Invalid username
Login to AoPS