If p and q are integers, is pq + 1 even?

Question

(1) If p is divided by 2, the remainder is 1.
(2) If q is divided by 6, the remainder is 1.

mendheypriyanka · Answer

For PQ+1 to be even, product of P and Q must be odd. For the product to be odd, P and Q both must be odd.

Option1: When P is divided by 2 and reminder is 1, implies P is odd. But nothing is mentioned about Q, so Q can be either even or odd. 
The statement is not sufficient.

Option2: When Q is divided by 6 and reminder is 1, implies Q is odd. But nothing is mentioned about P, so P can be either even or odd. 
The statement is not sufficient.

1+2: P and Q both are ODD, hence the PQ+1 will be even. 
The statement is sufficient.

So, the answer is 'C'.

mehrotrayashraj · Answer

Is pq + 1 even -> is pq odd -> are p and q odd

% -> Modulus sign, tells us what the remainder is 
p%2 -> 1 : Odd
p%6 -> 1 : 7,13,19,25,31,37... : Odd

Thus ans is C

sriamlan · Answer

Yes that is correct.

merajul · Answer

Question says is (pq+1) even

We denote any even no as 2n & any odd no as (2n+1)

(1) says, p=2a+1 => p must be odd, we do not know the value of q. So, INSUFFICIENT

(2) says, q=6b+1 => q=2*3b+1 =>q=2c+1 => q must be odd, we do not know the value of b. So, INSUFFICIENT

Combining (1) + (2), p*q = Odd (Since O*O =O)

Thus, (pq+1) = Odd +1 = Even. Option C is correct

bumpbot · Answer

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If p and q are integers, is pq + 1 even?

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