Data Sufficiency

Mjkourtis wrote:What is the hundredths digit of decimal z?
(1) the tenths digit of 10z is 2.
(1) the units digit of 1,000z is 2.

Hi Mjkourtis!

This is a fun question that might be easier to solve if we recognize one method of handling Digit questions. Rather than just try to imagine the number, I'm going to give it shape... Let's call it

A.BCDE

Where A is the units digit, B the tenths, C the 100ths, D the 1,000ths and E the 10,000ths. So the question wants the 100ths digit so the real question is WHAT IS C?

Now, lets take a look at the statements:

Statement 1: "the tenths digit of 10z is 2"
Well, when we multiply ANY number times 10, that just means we are going to move the decimal ONE space to the RIGHT. So we have...

A.BCDE ---> AB.CDE

And since they say the 10ths digit is 2, and C is the 10ths digit, so that means C=2...SUFFICIENT

Statement 2: "the units digit of 1,000z is 2"
Well, when we multiply ANY number times 1000, that just means we are going to move the decimal THREE spaces to the RIGHT. So we have...

A.BCDE ---> ABCD.E

And since they say the units digit is 2 and the units digit is D, that means D=2...INSUFFICIENT

The answer is therefore A.

Hope this helps!

Whit

Mjkourtis wrote:What is the hundredths digit of decimal z?
(1) the tenths digit of 10z is 2.
(1) the units digit of 1,000z is 2.

Let us assume that z = a.bcd. Here we can see that the hundredths digit of z is c. We have to find the value of c.

(1) The tenths digit of 10z is 2 implies 10z = 10 * a.bcd = ab.cd
The tenths digit of 10z is c. So c = 2; SUFFICIENT.

(2) The units digit of 1,000z is 2 implies 1000z = 1000 * a.bcd = abcd
The units digit of 1000z is d. So, d = 2 but we cannot find the value of c from here; NOT sufficient.

The correct answer is A.