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.
help required
This topic has expert replies
- AleksandrM
- Legendary Member
- Posts: 566
- Joined: Fri Jan 04, 2008 11:01 am
- Location: Philadelphia
- Thanked: 31 times
- GMAT Score:640
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.
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.
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
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.
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.
Going with that assumption, I don't see how we can do this question without looking at decimal expansions.
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:AleksandrM wrote: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.
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.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
- AleksandrM
- Legendary Member
- Posts: 566
- Joined: Fri Jan 04, 2008 11:01 am
- Location: Philadelphia
- Thanked: 31 times
- GMAT Score:640