If ,what is the value of x?

(1)  ~$2x=(\frac{x}{2})^3$~

(2)  ~$x=2^{x-2}$~

what is the value of ~$x^2-y^2$~?

(1)  ~$(x-y)^2=9$~

(2) ~$x+y=6$~

If ~$N$~ is positive odd integer, is ~$N$~ prime?

(1) ~$N =2^k+1$~ for some positive integer ~$k$~.

(2) ~$N $~= 2 and ~$N$~ +4 are both prime.

If ~$n$~ is the least of three differentintegers greater than 1, what is the value of ~$n$~?

(1) The product of the three integers is90.

(2) One of the integers is twice one ifthe other two integers.

 If ~$a$~ and ~$b$~ are positive integers, what is the value of the product ~$ab$~?

(1) The least common multiple of ~$a$~ and ~$b$~ is 48.

(2)The greatest common factor of ~$a$~ and ~$b$~ is 4.

 If ~$m$~ and ~$n$~ are positive integers, is ~$m + n$~ divisible by 4?

(1)  ~$m$~ and ~$n$~ are each divisible by 2.

(2)  Neither ~$m$~ nor ~$n$~ is divisible by 4.

In atwo-month survey of shoppers, each shopper bought one of two brands ofdetergent, ~$X$~ or ~$Y$~, in the first month and again bought one of these brands inthe second month. In the survey, 90 percent of the shoppers who bought Brand ~$X$~ in the first month bought Brand ~$X$~ again in the second month, while 60 percentof the shoppers who bought Brand ~$Y$~ in the first month bought Brand ~$Y$~ again inthe second month. What percent of the shoppers bought Brand ~$Y$~ in the secondmonth?

(1)  In the first month, 50 percent of theshoppers bought Brand ~$X$~.

(2)  The total number of shoppers surveyed was5,000.

Thearithmetic mean of a collection of 5 positive integers, not necessarilydistinct, is 9. One additional positive integer is included in the collectionand the arithmetic mean of the 6 integers is computed. Is the arithmetic meanof the 6 integers at least 10?

(1) Theadditional integer is at least 14.

(2) Theadditional integer is a multiple of 5.

 If ~$a$~ and ~$b$~ are constants,what is the value of ~$a$~?

(1) ~$a

(2) ~$(t-a) (t-b)$~ =~$t^2+t-12$~,  forall values of ~$t.$~

 Is ~$xm

(1) ~$ x>y$~

(2) ~$ m