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What is the hundredths digit of the decimal m?

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enigma123
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What is the hundredths digit of the decimal m? [#permalink] New post  Updated on: 20 Sep 2012, 04:27
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What is the hundredths digit of the decimal m?

(1) The tenths digit of 100m is 5.
(2) The tens digit of 1,000m is 5.
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Originally posted by enigma123 on 27 Feb 2012, 15:46.
Last edited by Bunuel on 20 Sep 2012, 04:27, edited 1 time in total.
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Re: Decimal m [#permalink] New post  27 Feb 2012, 15:56
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enigma123 wrote:
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.

The thing that confuses me is what do they mean by decimal m and then how that apply in 100m and 1000m. Can someone please explain?


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
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Re: Decimal m [#permalink] New post  27 Feb 2012, 16:12
Thanks very much Bunuel. I take it you mean m and not Z in your explanation above.
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Re: What is the hundredths digit of the decimal m? [#permalink] New post  29 Feb 2012, 02:04
Bunuel a quick question - can't the decimal be m = ab.cd? Why you have only picked m = a.bcd?
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Re: What is the hundredths digit of the decimal m? [#permalink] New post  29 Feb 2012, 02:13
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enigma123 wrote:
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.
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Re: What is the hundredths digit of the decimal m? [#permalink] New post  19 Nov 2016, 01:10
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
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Re: What is the hundredths digit of the decimal m? [#permalink] New post  24 May 2022, 07:39
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Re: What is the hundredths digit of the decimal m? [#permalink]
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