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

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
If p and q are integers, is pq + 1 even?  [#permalink]

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21 May 2017, 10:16
1
1
00:00

Difficulty:

5% (low)

Question Stats:

90% (01:11) correct 10% (01:20) wrong based on 135 sessions

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

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

_________________
Manager
Joined: 26 Jan 2016
Posts: 68
Location: India
GMAT 1: 690 Q49 V36
GPA: 3.01
Re: If p and q are integers, is pq + 1 even?  [#permalink]

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06 Jun 2017, 23:35
2
3
mendheypriyanka wrote:
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.

Yes that is correct.
##### General Discussion
Intern
Joined: 16 Apr 2017
Posts: 1
If p and q are integers, is pq + 1 even?  [#permalink]

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22 May 2017, 08:10
1
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.

Intern
Joined: 26 Jan 2017
Posts: 31
Re: If p and q are integers, is pq + 1 even?  [#permalink]

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22 May 2017, 10:39
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
Manager
Joined: 05 Oct 2014
Posts: 54
Location: India
Concentration: General Management, Strategy
GMAT 1: 580 Q41 V28
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Re: If p and q are integers, is pq + 1 even?  [#permalink]

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21 Oct 2017, 03:32
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
Re: If p and q are integers, is pq + 1 even? &nbs [#permalink] 21 Oct 2017, 03:32
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