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# What is the hundredths digit of the decimal z?

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What is the hundredths digit of the decimal z? [#permalink]  27 Apr 2010, 09:10
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What is the hundredths digit of the decimal z?

(1) The tenths digit is 100z is 2
(2) The units digit of 1,000z is 2
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Jan 2012, 08:06, edited 1 time in total.
Edited the question and added the OA
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Re: GMAT PREP (DS) [#permalink]  28 Apr 2010, 09:58
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What is the hundredths digit of the decimal z?

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

(1) The tenths digit is 100z is 2 --> $$100z=100*a.bcd=abc.d$$ --> the tenths digit of $$100z$$ is the value of $$d$$. So $$d=2$$. Not sufficient to calculate $$c$$.

(2) The units digit of 1,000z is 2 --> $$1000z=1000*a.bcd=abcd$$ --> the units digit of $$1000z$$ is the value of $$d$$. So $$d=2$$. Not sufficient to calculate $$c$$.

(1)+(2) No new info, only the value of $$d$$ is known. Not sufficient.

Note: 1234.567

1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS
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Re: GMAT PREP (DS) [#permalink]  28 Apr 2010, 12:08
I am sure Bunuel's explanation should have cleared your doubts, if there was any. But I pretty much followed the same what Bunuel explained.

Z = A.bcde

From stem, we should be able to find the value of 'c'

1. 100Z = A.bcde * 100 = Abc.de => tenth digit of 100z = d = 2, Not Sufficient to find the value of C
2. 100Z = A.bcde * 1000 = Abcd.e => units digit of 1000Z = d = 2, Not Sufficient to find the value of C

Both 1 and 2 are talking about 1000th digit of Z, which is Z. Hence, together 1 and 2, as well, we can not find the value of 100th digit of Z.

Hope this helps.
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Re: GMAT PREP (DS) [#permalink]  29 Apr 2010, 03:11
silly mistake went for hundred digit not hundredth
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Re: GMAT PREP (DS) [#permalink]  10 May 2010, 20:19
Bunuel wrote:
What is the hundredths digit of the decimal z?

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

(1) The tenths digit is 100z is 2 --> $$100z=100*a.bcd=abc.d$$ --> the tenths digit of $$100z$$ is the value of $$d$$. So $$d=2$$. Not sufficient to calculate $$c$$.

(2) The units digit of 1,000z is 2 --> $$1000z=1000*a.bcd=abcd$$ --> the units digit of $$1000z$$ is the value of $$d$$. So $$d=2$$. Not sufficient to calculate $$c$$.

(1)+(2) No new info, only the value of $$d$$ is known. Not sufficient.

When the question asks hundredths digit of the decimal z? , in that case, for example, $$z=xyz.bcd$$

x = hundredth digit
c = hundredth digit

How did you assume that the question is asking for C and not for X?
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Re: GMAT PREP (DS) [#permalink]  10 May 2010, 20:30
When the question asks hundredths digit of the decimal z? , in that case, for example,

$$z= xyz.bcd$$
x = hundredth digit
c = hundredth digit

How did you assume that the question is asking for C and not for X?

it is ....(Hundreds)(Tens)(Units).(tenths)(Hundredths)......

x = Hundreds digit
c = hundredths digit
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3. What is the hundredths digit of the decimal z?

(1) The tenths digit of 100z is 2
(2) The units digits of 100z is 2

Let the number, z be x.abcde. We need to find the hundredths digit of the decimal z which is the value of b.
Statement 1: 100z = xab.cde Given the tenth digit of 100z is 2 and hence c is 2.

Statement 2: 100z = xab.cde. Given the units digits of 100z is 2 and hence b is 2.

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Re: GMAT PREP (DS) [#permalink]  26 Apr 2011, 07:48
Let z = p.qr2s

(1)
100z = pqr.2s

We don't know "s".

(2)
1000z = pqr2.s

we don't know "s'

(1) and (2)

We don't know s.

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Re: GMAT PREP (DS) [#permalink]  26 Apr 2011, 09:00
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Re: What is the hundredths digit of the decimal z? [#permalink]  12 Jan 2014, 06:06
If it is asking for what is the hundredths digit of decimal z, isn't z just a digit between 0-9? In that case, isn't isn't any other digit besides the units digit of z=0? e.g. z= 09.00?

Let's assume z=9

1) 100z = 900.00; tenths digit = 0
2) 1000z = 9000.00; units digit = 0

D both alone are sufficient.
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Re: GMAT PREP (DS) [#permalink]  12 Jan 2014, 06:11
Expert's post
Bunuel wrote:
What is the hundredths digit of the decimal z?

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

(1) The tenths digit is 100z is 2 --> $$100z=100*a.bcd=abc.d$$ --> the tenths digit of $$100z$$ is the value of $$d$$. So $$d=2$$. Not sufficient to calculate $$c$$.

(2) The units digit of 1,000z is 2 --> $$1000z=1000*a.bcd=abcd$$ --> the units digit of $$1000z$$ is the value of $$d$$. So $$d=2$$. Not sufficient to calculate $$c$$.

(1)+(2) No new info, only the value of $$d$$ is known. Not sufficient.

Note: 1234.567

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

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Re: GMAT PREP (DS) [#permalink]  12 Jan 2014, 06:16
Bunuel wrote:
Bunuel wrote:
What is the hundredths digit of the decimal z?

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

(1) The tenths digit is 100z is 2 --> $$100z=100*a.bcd=abc.d$$ --> the tenths digit of $$100z$$ is the value of $$d$$. So $$d=2$$. Not sufficient to calculate $$c$$.

(2) The units digit of 1,000z is 2 --> $$1000z=1000*a.bcd=abcd$$ --> the units digit of $$1000z$$ is the value of $$d$$. So $$d=2$$. Not sufficient to calculate $$c$$.

(1)+(2) No new info, only the value of $$d$$ is known. Not sufficient.

Think I may just not understand what a decimal is. Why is decimal z not just a number from 0-9? Decimal z ≠ a digit?
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Re: GMAT PREP (DS) [#permalink]  12 Jan 2014, 06:26
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boyanshmorhun wrote:
Bunuel wrote:
Bunuel wrote:
What is the hundredths digit of the decimal z?

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

(1) The tenths digit is 100z is 2 --> $$100z=100*a.bcd=abc.d$$ --> the tenths digit of $$100z$$ is the value of $$d$$. So $$d=2$$. Not sufficient to calculate $$c$$.

(2) The units digit of 1,000z is 2 --> $$1000z=1000*a.bcd=abcd$$ --> the units digit of $$1000z$$ is the value of $$d$$. So $$d=2$$. Not sufficient to calculate $$c$$.

(1)+(2) No new info, only the value of $$d$$ is known. Not sufficient.

Think I may just not understand what a decimal is. Why is decimal z not just a number from 0-9? Decimal z ≠ a digit?

I think you should brush up fundamentals. Decimals and digits are not the same thing.

Decimal is a numbers that fall in between integers and expressed in terms of place value. For example, 3.4 , 1.7777, 7.8, ... are all decimals.

While digits are numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Hope it helps.
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Re: GMAT PREP (DS) [#permalink]  28 Jan 2014, 22:50
Let us say number is 0.abcd and the question asks the value of b?

Statement I is insufficient:

100z = ab.cd which says c = 2

Statement II is insufficient

1000z = abc.d which again says c = 2

Even by combining we are getting c = 2.

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Re: GMAT PREP (DS)   [#permalink] 28 Jan 2014, 22:50
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