What is the hundredths digit of the decimal m?

Let's say \(m=a.bcd\). The hundredths digit of z would be the value of \(c\). So the question is \(c=?\)

(1) The tenths digit is 100m is 5 --> \(100m=100*a.bcd=abc.d\) --> the tenths digit of \(100m\) is the value of \(d\). So \(d=5\). We need \(c\). Not sufficient.

(2) The tens digit of 1,000m is 5 --> \(1000m=1000*a.bcd=abcd\) --> the tens digit of \(1000m\) is the value of \(c\). So \(c=5\). Sufficient.

Answer: B.

Note: 1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS
_________________

Thanks very much Bunuel. I take it you mean m and not Z in your explanation above.
_________________

Bunuel a quick question - can't the decimal be m = ab.cd? Why you have only picked m = a.bcd?
_________________

Digits before decimal point doesn't matter for this problem. You can pick 0.abcd, 0.abc, 123.abc, ... it won't change the answer. We are just interested in hundredths digit of the decimal m, so when expressing it somehow make sure that you know which value are you looking for. For example for 123.abc it would be the value of b, you can substitute it in both statements to see that the answer will be exactly the same:

(1) The tenths digit is 100m is 5 --> 100m=123ab.c --> can not get b.
(2) The tens digit of 1,000m is 5 --> 1,000m=123abc --> b=5.

Hope it's clear.
_________________

Great Question
Let m=abc.pqr
So we actually need to find q
statement 1
tenths (100m) => tenths (abcpq.r)=> r=5
no clue of q
not sufficient
Statement 2
tens(1000m)=> tens(abcpqr)=> q=5
hence sufficient to say that hundredths digit of m must be
Hence B
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________