两道GWD MATH求解

cathyyan

    

求解题过程

GWD23-Q2:

    

The function f is defined for each
positive three-digit integer n by f(n) = 2^x 3^y
5^z, where x, y, and z are the
hundreds, tens, and units digits of n, respectively.  If m and v are three-digit
positive integers such that f(m) = 9 f(v), then m
- v =

    

 

    

A.    
8

    

B.     
9

    

C.     
18

    

D.    
20

    

E.     
80

    

Answer: D

    

GWD20-Q14:

    

Six cards numbered from 1 to 6 are placed
in an empty bowl.  First one card is
drawn and then put back into the bowl; then a second card is drawn.  If the cards are drawn at random and if the
sum of the numbers on the cards is 8, what is the probability that one of the
two cards drawn is numbered 5 ?

    

 

    

A.    
1/6

    

B.     
1/5

    

C.     
1/3

    

D.    
2/5

    

E.     
2/3

    

Answer: D

downtoearth

f(n) = 2^x 3^y 5^z    f(m) = 9 f(v)

m abc     v efg

f(v)= 2^e 3^d 5^f

f(m)= 2^a 3^b 5^c = 2^e 3^d 5^f 3² 
    

b = d +2 => b-d = 2

所以20

 

if the sum of the numbers on the cards is 8,  的有这几种情况 (2,6) (3,5)(4,4)(5,3)(6,2)

 one of the two cards drawn is numbered 5 ? (3,5) (5,3)

所以2/5

kenlin4590

同意