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Sunday, April 29, 2007
ALGEBRA QUESTION OF THE DAY
If p and q are different prime numbers and pq/2 is also a prime number, then p + q is (A) an odd number (B) an even number (C) a prime number (D) a negative number (E) not a prime number
Since pq/2 is prime, it is an integer. Hence, either p or q must be even; otherwise, the 2 would not cancel and pq/2 would be a fraction. The only even prime number is 2. Hence, either p or q, but not both, must be 2. The other one is an odd prime number. Now, the sum of an even number and an odd number is an odd number. The answer is (A).
E
ReplyDeletee
ReplyDeletei think E is wrong
ReplyDeletewhat if p=2 and q=3
pq/2 =3
p+q=5 … a prime number
i prefer A,
since pq/2 s prime refers either p or q is 2.
then p+q=2+q
where q is odd.
so asum will be always odd.
what is the answer?
Answer is A
ReplyDeleteThis comment has been removed by the author.
ReplyDeletemadhur is right.
ReplyDeleteA
Since pq/2 is prime, it is an integer. Hence, either p or q must be even; otherwise, the 2 would not
ReplyDeletecancel and pq/2 would be a fraction. The only even prime number is 2. Hence, either p or q, but not both,
must be 2. The other one is an odd prime number. Now, the sum of an even number and an odd number is
an odd number. The answer is (A).