Question 824763
NOT A:
If x, rounded to the nearest thousandth is 0.455,
{{{0.4545<=x<0.4555}}} ,
because {{{0.4545<=x<0.455}}} would be rounded up to {{{0.455}}} ,
and {{{0.455<x<4.555}}} would be rounded down to {{{0.455}}} ,
but {{{x<0.4545}}} would be rounded down to {{{0.454}}} ,
and {{{x>=0.4555}}} would be rounded up to {{{0.456}}} .
That is not enough information to find the result when x is rounded to the nearest hundredth,
because when rounding to the nearest hundredth,
{{{0.4545}}} , or {{{0.4547}}} ,
or any number {{{x}}} such that {{{0.4545<=x<0.455}}} ,
would be rounded down to {{{0.45}}} ,
but {{{0.455}}} , or {{{0.4554}}} ,
or any number {{{x}}} such that {{{0.455<=x<4.555}}} ,
would be rounded up to {{{0.46}}} .
 
NOT B (at least not the way I read it):
If {{{x=0.005}}} the thousandths digit of x is 5,
but the result when x is rounded to the nearest hundredth is {{{0.01}}} .
There are many numbers that have a 5 for the thousandths digit
We need to know the other digits too.
If the higher value digits were {{{0.45}}} ,
it could be {{{"0.4550"<=x<0.46}}} , which would round up to {{{0.46}}}.
 
{{{highlight(C)}}}= (1) AND (2) TOGETHER:
(1) means that {{{0.4545<=x<0.4555}}}
(1) along with (2) means that {{{"0.4550"<=x<0.4555}}} ,
and {{{x}}} would round up to {{{0.46}}} for sure.
 
WARNING:
If by "(2) The thousandths digit of x is 5" we are supposed to assume that we somehow know that the digits to the left of the thousandths digit are {{{0.45}}} ,
then B would be the answer.