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If p and q are different prime numbers and a, b, and c are consecutive
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14 Jan 2023, 22:02
1
Given that p and q are different prime numbers and a, b, and c are consecutive integers such that a < b < c and we need to find which of the following must be odd
Since p and q are different prime numbers So, p can be 2 (Even) or any other odd prime number q can be 2(if p is not 2) or any other odd prime number apart from what p is => Either of p or q can be even or both can be odd too.
a, b, c are consecutive integers such that a < b < c => if a is odd then b is even and c is odd => if a is even then b is odd and c is even => a and c will be either both odd or both even, and b will be even or odd accordingly
(A) ap Now, p can be even => ap can be even => FALSE
(B) bp Now, p can be even => bp can be even => FALSE
(C) pq Now, p can be even => pq can be even => FALSE
(D) a + b Now, a can be odd, making b as even and we know odd + Even = odd a can be even, making b as odd and we know even + odd = odd => a + b will ALWAYS be odd => TRUE
(E) a + q Now, both a and q can be odd or both can be even making a + q = even => FALSE
So, Answer will be D Hope it helps!
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