Hello all, was having some trouble with the following questions. Since GMAT Prep doesn't provide explanations, what better place to ask than at beatthegmat? here goes.

2. xy+z=x(y+z), which of the following must be true?
A) x=0 and z=0
B) x=1 and y=1
C) y=1 and z=0
D) x=1 or y=0
E) x=1 or z=0

OA E

3. For every integer K from 1 to 10 inclusive, the kth term of a certain sequence is given by
(-1)^k+1(1/2^k). If T is the sum of the first ten terms in the sequence, then T is,

A) Greater than 2
B) Between 1 and 2
C) Between ½ and 1
D) Between ¼ and ½
E) Less than ¼

OA E

Removed a question after seeing it on a separate thread.

18. For which of the following functions f is f(x)=f(1-x) for all x?

A) f(x)=1-x
B) f(x)=1-x^2
C) f(x)=x^2-(1-x^2)
D) f(x)=x^2(1-x)^2
E) f(x)=x/1-x

OA D

31. When a certain tree was first planted it was 4 feet tall and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, it was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

A) 3/10
B) 2/5
C) ½
D) 2/3
E) 6/5

OA D

Please show all calculations and explain OA's. Will post DS in DS forum. Thanks in advance!