Difference between revisions of "2011 AMC 8 Problems/Problem 17"

Latest revision as of 14:08, 17 December 2023

Let $w$ , $x$ , $y$ , and $z$ be whole numbers. If $2^w \cdot 3^x \cdot 5^y \cdot 7^z = 588$ , then what does $2w + 3x + 5y + 7z$ equal?

$\textbf{(A) } 21\qquad\textbf{(B) }25\qquad\textbf{(C) }27\qquad\textbf{(D) }35\qquad\textbf{(E) }56$

The prime factorization of $588$ is $2^2\cdot3\cdot7^2.$ We can see $w=2, x=1,$ and $z=2.$ Because $5^0=1, y=0.$

$2w+3x+5y+7z=4+3+0+14=\boxed{\textbf{(A)}\ 21}$

~savannahsolver

2011 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 16	Followed by Problem 18
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

@@ Line 19: / Line 19: @@
 ~savannahsolver
+==Video Solution 4 by SpreadTheMathLove==
+https://www.youtube.com/watch?v=mYn6tNxrWBU
 ==See Also==
 {{AMC8 box|year=2011|num-b=16|num-a=18}}
 {{MAA Notice}}