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

 If ~$x$~>0, what is the value of ~$x$~?

(1) ~$x^3-x=0$~

(2) ~$\sqrt[3]{x}-x=0$~

 If ~$m$~ is an integer greater than 1, is ~$m$~ an even integer?

(1) 32 is a factor of ~$m$~.

(2)  ~$m$~ is a factor of 32.

Is ~$x>y$~?

(1) ~$x+y>x-y$~

(2)~$3y>2y$~

 How much did credit-card fraud cost United States banks in year ~$X$~ to the nearest $10 million?

(1) In year ~$X$~, counterfeit cards and telephone and mail-order fraud accounted for 39 percent of the total amount that card fraud cost the banks.

(2)In year ~$X$~, stolen cards accounted for $158.4 million, or 16 percent, of the total amount that credit-card fraud cost the banks

Rita’s monthly salary is ~$\frac{2}{3}$~  Juanita’s monthly salary. What is theircombined monthly salary?

(1) Rita’s monthly salary is $4,000.

(2) Either Rita’s monthly salary or Juanita’s monthly salary is $6,000.