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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]

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Updated on: 05 Jun 2019, 04:23
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Difficulty:

25% (medium)

Question Stats:

72% (01:26) correct 28% (01:26) wrong based on 671 sessions

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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

Originally posted by LM on 27 Apr 2010, 10:10.
Last edited by Bunuel on 05 Jun 2019, 04:23, edited 2 times in total.
Edited the question and added the OA
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Joined: 02 Sep 2009
Posts: 58095
Re: What is the hundredths digit of the decimal z?  [#permalink]

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28 Jan 2012, 09:04
48
46
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: What is the hundredths digit of the decimal z?  [#permalink]

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28 Apr 2010, 10:58
17
23
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: What is the hundredths digit of the decimal z?  [#permalink]

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12 Jan 2014, 07:16
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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Posts: 58095
Re: What is the hundredths digit of the decimal z?  [#permalink]

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12 Jan 2014, 07:26
1
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: What is the hundredths digit of the decimal z?  [#permalink]

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28 Jan 2014, 23:50
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: What is the hundredths digit of the decimal z?  [#permalink]

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18 Apr 2017, 17:07
1
Top Contributor
1
LM wrote:
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

Target question: What is the hundredths digit of the decimal z?

Statement 1: The tenths digit of 100z is 2
Notice what happens when we take a decimal like 0.123456 and multiply it by 100.
We get 12.345 (the tenths digit is 3)
In the original decimal, the 3 was in the thousandths place.
So, statement 1 tells us that the THOUSANDTHS digit of z is 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The unit digit of 1000z is 2
Notice what happens when we take a decimal like 0.123456 and multiply it by 1000.
We get 123.45 (the units digit is 3)
In the original decimal, the 3 was in the thousandths place.
So, statement 2 tells us that the THOUSANDTHS digit of z is 2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

NOTE: Since statements 1 and 2 BOTH tell us the same thing (i.e., the THOUSANDTHS digit of z is 2), the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: What is the hundredths digit of the decimal z?  [#permalink]

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25 Sep 2017, 18:48
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

How did u get z =2? Pls help..
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Posts: 58095
Re: What is the hundredths digit of the decimal z?  [#permalink]

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25 Sep 2017, 20:53
zanaik89 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.

Note: 1234.567

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

How did u get z =2? Pls help..

We got that d = 2, not z. d is a THOUSANDTHS digit of z (z=a.bcd) so the TENTHS digitt of 100z (100z=100*a.bcd=abc.d), which in (1) we are told to be 2.

P.S. Please do NOT double-post. Thank you.
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Re: What is the hundredths digit of the decimal z?  [#permalink]

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01 Sep 2019, 23:06
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Re: What is the hundredths digit of the decimal z?   [#permalink] 01 Sep 2019, 23:06
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