help required

[vaivish]

If n is a positive integer less than 10, n=?
(1) n is equal to the tens' digit of 1/n.
(2) n is equal to the hundreds' digit of 1/n.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

[ksh]

IMO picking numbers can work !

lets pick up a positive integer 3 by hit and trial.

Stem 1: n equals tenth digit 1/3=0.33 suff
Stem2: n equals hundreth digit, suff

So, D

[AleksandrM]

I will have to go with E.

If n is less than 10, then 1/n could be 1/9 = 1 in tens digit or 1/4 = 2 in the tens digit.

Same goes for 1/n for the second statement 1/2 = 0 in hundreds digit and 1/8 = 2 in the hundreds digit.

[vaivish]

OA its A...as the tens digit is same ...it has to be 3...but why the statement B is not helping...becasue its 0.333 and its 3 again....

[Ian Stewart]

I think the question means to refer to the 'tenths' digit and the 'hundredths' digit, because 1/n does not have a 'tens digit' or 'hundreds digit' if n is a positive integer.

Going with that assumption, I don't see how we can do this question without looking at decimal expansions.

I will have to go with E.

If n is less than 10, then 1/n could be 1/9 = 1 in tens digit or 1/4 = 2 in the tens digit.

Same goes for 1/n for the second statement 1/2 = 0 in hundreds digit and 1/8 = 2 in the hundreds digit.

The logic above is incorrect; n cannot be 9, because the tenths digit of 1/9 is equal to 1, not 9. Let's look at what values n might have:

1) If n = the tenths digit of 1/n, then n cannot be 1 or 2, but n might be 3. But as you make n larger than 3, the tenths digit of 1/n gets smaller: it's equal to either 1 or 2, depending on n. So the tenths digit of 1/n is only equal to n when n=3; sufficient.

2) If n = the hundredths digit of 1/n, we have more work to do. Certainly, n might be equal to 3, since 1/3 = 0.3333..... But, as we check the other decimal expansions, we discover that n might be equal to 6, since 1/6 = 0.166666.... So we have more than one choice for n: insufficient.

A.

[AleksandrM]

Oops. Thanks Ian. I misread the statements.