If is a prime integer less than or equal to then is prime.
How many counter-examples are there to the above claim?
(A)
(B)
(C)
(D)
(E)
A real number is called nearly-even, if there is an even integer such that
If is a nearly-even number, which of the following statements must be true?
(A) II only
(B) I and II only
(C) I and III only
(D) II and III only
(E) None of the statements
If is prime, then is also prime.
Which of the following is a counter-example of the above claim?
(A)
(B)
(C)
(D)
(E)
A number is called 4-average if it is the average of four positive integers. If is a 4-average number, which of the following statements is true?
(A) II only
(B) III only
(C) II and III only
(D) I, II, and III
(E) None of the statements
If then
Which of the following is a counter-example of the above claim?
(A)
(B)
(C)
(D)
(E)