What is the hundredths digit of the decimal m?

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

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

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

Hope it helps.
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B.

What is the hundreths digit of the decimal m ?
(1) The tenths digit of 100m is 5.
(2) The tens digit of 1,000m is 5.

To solve this lets randomly say that m = .05.

(1) 100 (.05) = 5.00 => 0 does not equal 5 (which is our hundreths digit) so A is insufficient
(2) 1000 (.05) = 50.00 since the 5 is in the tens digits and 5 = 5 we have a winner.

B is sufficient.

What is the hundreths digit of the decimal m ?
(1) The tenths digit of 100m is 5.
if we take m = 0.005, thus the tenths digit of 100m is 5
and the hundreths digit of the decimal m is 0
Why is it not sufficient ?
How do you know that the tenths digit must be equal to the hundreths digit ?

Once you are past zero it goes tenths, hundredths, thousandths
So in the number 0.05 the number 5 is in the hundredths position. In 0.5 the number 5 is in the tenths position.

Taking this knowledge if something is in the hundredths position (meaning in the 0.0X location) and you multiply it by 1,000 you are shifting the decimal place three spaces to the right.

We started out at 000.0x and we end up shifting it to 0X0.00.

So by multiplying the hundredths position by 1,000 the digit shifts its location to the tens position.

Does this make sense or did I butcher that explanation?

thanks
with a.bcd it is much clearer for me

Nice one. I had missed basic basic math...was doing units, tenths, hundreths..

I also missed this one. Nice Refersher on Basic concepts.

I forgot that after decimal point it is th tenths, hundred etc..
so got the wrong answer..
thank u bennel...

Let m be abc.pqr
So we need to get q
statement 1
100m=abcpq.r
tenths digit of 100m => 5
hence r=5
hence insufficient
statement 2
1000m=abcpqr
tens 1000m=q
hence q=5
hence sufficient
Hence B
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\(m=12.3456 \implies 100m=1234.56\) we need a match with 4, however.

\(m=12.3456 \implies 1000m=12345.6\) we get a match with 4!
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Bunuel, I am guessing for these types of questions, the way you've defined the decimal is by cheating and looking at the statements?
e.g. statement 2 says 1000 x m so you know you will have to move things over 3 decimal places, hence m should start with 3 decimal places?
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