If x, y, and z are integers and (2^x)(5^y)z = 0.00064, what is the value of xy?
(1) z = 20
(2) x = –1
(1) z = 20
(2) x = –1
IMO Aavenus wrote:If x, y, and z are integers and (2^x)(5^y)z = 0.00064, what is the value of xy?
(1) z = 20
(2) x = –1
(2^x)(5^y)z = 64/(10^5)
(2^x)(5^y)z=(2^6)/[(2^5)*(5^5)]..splitting 10^5 into 2^5*5^5
(2^x)(5^y)z=2/(5^5)=(2)*(5^-5)
1. Z=(2^2)*5
substitute z in above eqtn
(2^x)(5^y)=[(2)*(5^-5)]/[ (2^2)*5]=(2^-1)*(5^-6)
2^1 in Numberator and 2^2 in denominator hence effectively 2^(1-2)=2^-1
similarly 5^-5 in numr and 5^1 in denominator hence 5^(-1-1)=5^-6
x=-1, y=-6 calculate xy sufficient
2. we know x=-1
(2^x)(5^y)z==(2)*(5^-5)
z=(2^2)*[5^(-5+y)]
for z to be an integer, y can be any integer >=5
hence xy could change
