Interesting, I've never seen a problem like this before but I'll give it a shot...

Looking at it from the set perspective (which is my preferred strategy), the allowable set from the stem is

{.95, .85, .75, ..., .05}

Lets see how each of the statements alter that

(1) r < 1/3
this lessens the set to

{.25, .15, .05}

this is insufficient since the set still contains multiple values

(2) r < 1/10
the set is now

{.05}

there is a single number left in the possible set (this statement restricts t to 0) so this is sufficient.

Edit: Now that I think about it, I would pick (C) 'cause the decimal 0.t5 doesn't have the minus sign (-) before 0, thus I guess it should be a positive decimal...

IMO [spoiler](E)[/spoiler], BUT if there's a constraint that "r" must be a positive number, then I would change my answer to [spoiler](C)[/spoiler]

r = 0.t5(decimal) t=?

1) r < 1/3
r < 0.33...

r could be 0.25, 0.15, 0.05, -0.05, -0.15, -0.25, -0.35 etc...
So t could be any number...

2) r < 1/10
r < 0.10

r could be 0.05, -0.05, -0.15, -0.25, -0.35 etc...
So t could be again any number...

1) and 2) Combined:
r could be 0.05, -0.05, -0.15, -0.25, -0.35 etc...
As we saw, t could be any number...

anartey wrote:If r is represented by the decimal 0.t5 what is the digit t ?

1) r < 1/3
2) r < 1/10

Can't seem to wrap my mind around the solution. Thanks for your help.

MAAJ wrote:Edit: Now that I think about it, I would pick (C) 'cause the decimal 0.t5 doesn't have the minus sign (-) before 0, thus I guess it should be a positive decimal...

Yeah I don't think that a digit has a sign and thus can't change the sign of the entire number. But I may be wrong...