hundreth digit

[naveenhv]

What is the hundredths digit of the decimal z?

1) The tenths digit of 100z is 2

2) The units digit of 1000z is 2

[smohit04]

E.

from both the options we can determine that the decimal z is of type x.xx2 but we could not determine the hundredths place from either/both options.

[RonPurewal]

(1) The tenths digit of 100z is 2

this means that you can write
100z = ......xxxxxxxx.2xxxxxxxx..... (where the letters are digits)
so, dividing by 100 gives
z = ....xxxxxx.xx2xxxxxxxx... (because division by 100 moves the decimal 2 spots over)
the hundredths digit here is still an unknown mystery digit -- we only know that 2 is the thousandths digit of z -- so, insufficient.

(2) The units digit of 1000z is 2

this means that you can write
1000z = ......xxxxxxxx2.xxxxxxxx..... (where the letters are digits)
so, dividing by 1000 gives
z = ....xxxxxx.xx2xxxxxxxx... (because division by 1000 moves the decimal 3 spots over)
again, the hundredths digit here is still an unknown mystery digit -- we only know that 2 is the thousandths digit of z -- so, insufficient.

together:
we still have the same information given by either statement alone, and nothing new.
still insufficient.

(e)

[naveenhv]

Thanks a ton Ron. Thats an excellent approach for this problem. Makes it so easy to digest.

[jnelson0612]

Great. :-)

[BernardK777]

When a problem refers to a decimal, should we assume that it can be a decimal number? In this I problem, I thought z was just a decimal and thus less than 1 and got the problem wrong.

Thanks for the help.

[RonPurewal]

When a problem refers to a decimal, should we assume that it can be a decimal number? In this I problem, I thought z was just a decimal and thus less than 1 and got the problem wrong.

Thanks for the help.

The answer to the problem is the same either way.

The only digits involved in the statements are digits that appear to the right of the decimal point in the original number z. So, it doesn't matter whether there is anything to the left of the decimal point.

[BernardK777]

Ron,

Thanks for your response! I understand what you mean. I think I was misunderstanding that if a number is a decimal it doesn't have to be less than 1. For example, 1.2 is a decimal right?

Because when I originally approached statement 1:

I thought 100z had to be less than 1, concluding that

100z = .2xxxxxx
z = .0002xxxx --> Sufficient


I understand why this is wrong now though. 100z can have digits to the left of the decimal as shown in your example.

[tim]

"Decimal" is just a way of saying the number is not a fraction. Either a decimal or a fraction can be greater than 1.

[RonPurewal]

Ron,

Thanks for your response! I understand what you mean. I think I was misunderstanding that if a number is a decimal it doesn't have to be less than 1. For example, 1.2 is a decimal right?

Because when I originally approached statement 1:

I thought 100z had to be less than 1, concluding that

100z = .2xxxxxx
z = .0002xxxx --> Sufficient


I understand why this is wrong now though. 100z can have digits to the left of the decimal as shown in your example.

The problem states that z, NOT 100z, is a "decimal". If you assume that z < 1, there is no change in the answer to the problem.
As for whether 100z is a "decimal", the problem specifies nothing, so you should assume nothing.

If you assume that 100z is a decimal, then you're in trouble. But you'll always be in trouble if you assume properties where none are specified at all.

[tim]

But you'll always be in trouble if you assume properties where none are specified at all.

Very good advice - and it works every bit as well for Sentence Correction too!

[RonPurewal]

But you'll always be in trouble if you assume properties where none are specified at all.

Very good advice - and it works every bit as well for Sentence Correction too!

^^ I'm curious—I don't see an immediate analogy to sentence correction. In this analogy, what is analogous to "properties"?

[tim]

Grammar rules! You and I are both well aware of a few forum users who make up non-existent grammar rules left and right just like some people make up math properties that aren't specified in our materials. :)

[RonPurewal]

I see.

Yes, definitely.