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If r and s are both positive integers, is the product of r and s even?

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If r and s are both positive integers, is the product of r and s even?  [#permalink]

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New post 21 Aug 2018, 13:22
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A
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D
E

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If r and s are both positive integers, is the product of r and s even?

(1) r and s are consecutive integers.

(2) (s - 1) is a prime number greater than 3.

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Re: If r and s are both positive integers, is the product of r and s even?  [#permalink]

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New post 21 Aug 2018, 13:31
S1: out of two consecutive integers, one will always be even, hence their product will be even. Sufficient

S2: any prime number greater than 3 is odd and hence will be followed by an even number. Hence s-1 is odd and s is even. Hence, the product of r and s will be even. Sufficient.

I vote that the answer is d

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If r and s are both positive integers, is the product of r and s even?  [#permalink]

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New post Updated on: 21 Aug 2018, 13:41
Bunuel wrote:
If r and s are both positive integers, is the product of r and s even?

(1) r and s are consecutive integers.

(2) (s - 1) is a prime number greater than 3.


(1) r and s are consecutive integers.
This case will always result in an even number
sufficient.

(2) (s - 1) is a prime number greater than 3.
say
s=6
as even * odd/even=even

D

corrected thanks !!

Originally posted by CounterSniper on 21 Aug 2018, 13:35.
Last edited by CounterSniper on 21 Aug 2018, 13:41, edited 1 time in total.
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Re: If r and s are both positive integers, is the product of r and s even?  [#permalink]

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New post 21 Aug 2018, 13:38
1
CounterSniper wrote:
Bunuel wrote:
If r and s are both positive integers, is the product of r and s even?

(1) r and s are consecutive integers.

(2) (s - 1) is a prime number greater than 3.


(1) r and s are consecutive integers.
This case will always result in an even number
sufficient.

(2) (s - 1) is a prime number greater than 3.
say
s=6
r=?
insufficient .

A


I don't think the value of r should matter if it's proved that s is even, since any number multiplied by an even number is even

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If r and s are both positive integers, is the product of r and s even?  [#permalink]

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New post 21 Aug 2018, 13:56
Bunuel wrote:
If r and s are both positive integers, is the product of r and s even?

(1) r and s are consecutive integers.

(2) (s - 1) is a prime number greater than 3.



we are looking for the the product of rs, whether it's even or not.

Statement 1: r ans s are consecutive integers. r= 2 s = 3. rs = 6. Sufficient.

Statement 2: s - 1 = prime. Note: only even prime is 2. So, s has to be an even number for sure. even * odd / even = even .


The best answer is D.
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Re: If r and s are both positive integers, is the product of r and s even?  [#permalink]

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New post 21 Aug 2018, 19:52
Bunuel wrote:
If r and s are both positive integers, is the product of r and s even?

(1) r and s are consecutive integers.

(2) (s - 1) is a prime number greater than 3.


r*s =?

(1) r and s are consecutive integers.

For any consecutive integers one has to be even and odd

Hence even*odd=even

Suff

(2) (s - 1) is a prime number greater than 3

If (s-1) is prime number s has to be even

Hence Suff

Hence D
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Re: If r and s are both positive integers, is the product of r and s even? &nbs [#permalink] 21 Aug 2018, 19:52
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