Numbers

Let the numbers x and y satisfy the conditions:

\(x^2+y^2-xy=2\)

\(x^4+y^4+x^2y^2=8\)

The value of \(P=x^8+y^8+x^{2014}\times y^{2014}\) is:

In the United States, Thanksgiving is celebrated on the fourth Thursday in November. Which of the following statements is (are) true?

I. Thanksgiving is always the last Thursday in November.

II. Thanksgiving is never celebrated on November 22.

III. Thanksgiving can not be celebrated on the same date 2 years in a row

In the figure at the right, how many paths are there from A to X

if the only ways to move are up and to the right? 

(A) 4          (B) 5          (C) 6           (D) 8         (E) 9

If 0< a< b< 1. which of the following is (are) true?

I. a- b is negative

II.  \(\dfrac{1}{ab}\) is positive

III. \(\dfrac{1}{b}\) - \(\dfrac{1}{a}\) is positive

(A) I only           (B) II only           (C) III only           (D) I and II only          (E) I, II and III

3; 6; 9; 12; 15; 18; 21; 24; 27; 30; ...

Which number are in 99th place?