Statement one

(x + 1/x) /2 = (y +1/y)/2

(x^2 + 1)/x = (y^2 +1)/y

cross multiplying

x^2y + y = xy^2 + x

x(xy-1)= y(xy-1)

Hence if xy is not equal to -1 then x = y but we dont know whether xy is -1 or not
Hence Insuff

Statemnet two

Tells us xy = 1

It can be 1/3 * 3 which are not equal hence Insuff

Combined
We needed the value of xy -1 which we get from 2 which is zero

Hence Insuff

IMO E

gmatmachoman wrote:Does x = y ?

(1) The average of x and 1/x equals the average of y and 1/ y

.
(2) xy = 1

statement 1:
x + 1/x = y + 1/y
2 possibilities: x=y or x=1/y. hence insufficient

statement 2:
x=1/y
2 possibilities: if y=1, x=y but if y is anything else x is not equal to y

combining the above two is not giving any new information... if x=1/y then mean of x+1/x will be equal to mean of y+1/y
hence the doubt stays i.e. if y=1, x=y but if y is anything else x is not equal to y

hence both statements are not sufficient to answer !

gmatmachoman wrote:Does x = y ?

(1) The average of x and 1/x equals the average of y and 1/ y

.
(2) xy = 1

2) => y = 1/x

in which case x=y when x=y=1

when x=y=1 1) and 2 are satisfied
when x = 1/2 and y =2 1 and 2 are satisfied

we cant say anything about whether x =y even when both statements are true

so E

eaakbari wrote:Statement one
(x + 1/x) /2 = (y +1/y)/2
(x^2 + 1)/x = (y^2 +1)/y
cross multiplying
x^2y + y = xy^2 + x
x(xy+1)= y(xy+1)
Hence if xy is not equal to -1 then x = y but we dont know whether xy is -1 or not
Hence Insuff
IMO C

got to recheck the bold part
x²y+y = xy²+x
x²y -x = xy² - y
x(xy-1) = y(xy-1)
from (2) we know xy -1 = 0

IMO C -- What is the OA?

IMO E what is the OA.

kstv wrote:

eaakbari wrote:Statement one
(x + 1/x) /2 = (y +1/y)/2
(x^2 + 1)/x = (y^2 +1)/y
cross multiplying
x^2y + y = xy^2 + x
x(xy+1)= y(xy+1)
Hence if xy is not equal to -1 then x = y but we dont know whether xy is -1 or not
Hence Insuff
IMO C

got to recheck the bold part
x²y+y = xy²+x
x²y -x = xy² - y
x(xy-1) = y(xy-1)
from (2) we know xy -1 = 0

Thanks for pointing that out. Silly mistakes , Silly mistakes. Edited it.
Answer does change
E
Thanks again kstv

Please give OA gmatmachoman