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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.

Answer: E.

Note: 1234.567

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

Answer is E.
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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

Answer:

Cheers,
Brent
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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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Bunuel ,

Why there is no multiplication sign between 100& Z ! When I saw this question in GMATPREP test, I got confused and I thought 100Z is one number

If 100z were a four-digit number it would have been mentioned explicitly. Without that, 100z can only be 100*z, since only multiplication sign (*) is usually omitted.
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Let, z=a.bcdefg, we need to know what is c?

(1) \(a.bcdefg*100=abc.defg\); Given that \(d=2\), but \(e\) (the hundredths digit) can be any digit. Insufficient.

(2) \(a.bcdefg*1000=abcd.efg\); Given that \(d=2\), \(f\) (the hundredths digit) can be any digit. Insufficient.

Considering both:
We get for both options \(d=2\) but we can't define \(e \ or \ f\) in either case. Insufficient.

The answer is \(E\)
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