Discussion Forum

Need help with an AMC8 mock question

 
 
SongAshley的头像
Need help with an AMC8 mock question
SongAshley - 2017年10月22日 Sunday 16:32
 

Let ww, xx, yy, and zz be whole numbers. If 2^w⋅3^x⋅5^y⋅7^z=5882w⋅3x⋅5y⋅7z=588, 

then what does 2w+3x+5y+7z2w+3x+5y+7z equal?

(A) 21(B) 25(C) 27(D) 35(E) 56(A) 21(B) 25(C) 27(D) 35(E) 56

Could someone please help explain how to solve this problem? THanks!

 
SongAshley的头像
Re: Need help with an AMC8 mock question
SongAshley - 2017年10月22日 Sunday 16:33
 

When I tried to copy and past, it looks normal, but them when I saved it, it is duplicated and formatted weird. 

 
显示父帖
AdminZIML的头像
Re: Need help with an AMC8 mock question
AdminZIML - 2017年10月26日 Thursday 10:19
 

What have you tried so far Ashley?

One good place to start is noticing that the powers on the left are all prime numbers. So, how does $588$ look like when you factor it out using prime numbers?

 
显示父帖
LiuAnna的头像
Re: Need help with an AMC8 mock question
LiuAnna - 2017年10月27日 Friday 11:54
 

2, 3, 5, and 7 are prime numbers. The prime factorization of 588 is 2^2 x 3 x 7^2. 3= 3^1, and since there is no five, you write it as 5^0. 2(2) + 3(1) + 5(0) + 7(2) = 4 + 3 + 0 + 14 = 21, so the answer would be (a) 21. 

 
显示父帖