pichitrat wrote:
If x is a positive integer and <z> is the greatest multiple of ten less than or equal to z, what is the value of x-<x>?
(1) <x^14> + x^15 has a units digit of 7
(2) <x^15> + x^16 has a units digit of 1
x-<x> is asking for the units
ie. x,<x>=33,30; x,<x>=51,50
(1) sufic
cycles of 3: 3,9,27,81.. [3,9,7,1]
cycles of 7: 7,49,343,___1.. [7,9,3,1]
cycles of 9: 9,1.. [9,1]
units(x^15)=7, 15/{4,2} has rem {1,3}
if units x=3: 3^15 has units of 7 correct
if units x=7: 7^15 has units of 3 invalid
if units x=9: 9^15 has units of 9 invalid
units of x is 3
(2) insufic
cycles of 1: always [1]
cycles of 3: [3,9,7,1]
cycles of 7: [7,9,3,1]
cycles of 9: [9,1]
units(x^16)=1, 16/{4,2,1} has rem 0
if units x=1: 1^16 has units of 1 correct
if units x=3: 3^16 has units of 1 correct
if units x=7: 7^16 has units of 1 correct
if units x=9: 9^16 has units of 9 invalid
units x could be {1,3,7}
ans (A)