What is the hundredths digit of the decimal m?

Question

(1) The tenths digit of 100m is 5.
(2) The tens digit of 1,000m is 5.

Bunuel · Answer

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

enigma123 · Answer

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

enigma123 · Answer

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

Bunuel · Answer

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

Hope it's clear.

stonecold · Answer

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

bumpbot · Answer

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What is the hundredths digit of the decimal m?

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