What is the hundredths digit of the decimal z?

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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.

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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Bunuel
just want to confirm, Is it the extra "TH" in the end to differentiate whether its talking before the decimal point or after?
for example 123.45, here Tens digit is 2 and Tenth digit is 4. Hence, an extra "TH" is responsible to avoid confusion ?
Right?

Right.




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