Question

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 the pizza they consumed?

Alex, Beth, Cyril, Dan

Beth, Cyril, Alex, Dan

Beth, Cyril, Dan, Alex

Beth, Dan, Cyril, Alex

Dan, Beth, Cyril, Alex

Solution:

Since $\frac 13 > \frac 14 > \frac 15,$ we know Beth ate more than Cyril and Cyril ate more than Alex. Thus, those three are in order.

The amount Dan ate is $1- \dfrac 13 - \dfrac 14 - \dfrac 15 = \dfrac{13}{60}.$ This is greater than $\frac 15$ and less than $\frac 14 ,$ so Dan is in between Cyril and Alex. This makes the order Beth, Cyril, Dan, Alex.

Thus, the correct answer is C .

2015 AMC 10B Problem 4

Solution:

Problem 4 in Other Years