PROBLEM 1:
Statement 1 tells us that n is non-zero. However, we could have cases like -1^2=1 or 1^2=1, so we do not have sufficient information to find one solution for z.
Statement 2 tells us that z>0. However, we could have cases like 3^0=1 and 1^2=1. So, we don't have a single answer for z and the statement is not sufficient.
Putting the statements together, we know we do NOT have the case that z^0=1 or the case -1^something even =1. The only other way we can get an answer of 1 is to have 1^something =1. Thus, z=1 and with both statements together we have sufficient info so the answer is C.
PROBLEM 2:
z is of the form .abc, where a is the tenths digit, b is the hundreths digit (what we are solving for) and is the thousandths digit. Yes, z may have more digits on either side of the decimal, but you will see these are the only digits that matter.
From statement 1, we know the tenths digit of 100z is 2. 100z = ab.c, so c=2. We wanted to solve for b, and do not have sufficient information.
From statement 2, we know the units digit of 1000z is 2. 1000z = abc, so c=2. Again, this does not help us solve for b so we do not have sufficient info.
Putting the statements together, we only have sufficient info to solve for c but not for b. Since we do not have sufficient info, the answer is E.
Tatiana Becker | GMAT Instructor | Veritas Prep
