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

Hi,
can someone explain why didn't we consider x=0 as a possible value while analysing the 1st statement.
We do consider 0 as an integer and as per the question stem , x and s are positive integers.

If that's the case , then 0+3= 3 (prime number) and the product of x and s will be zero. What should we consider zero here then?

Two points here:
1. We are told that x and s are both positive integers. 0 is neither positive nor negative number.
2. If x = 0, then xs = 0 = even. Recall that 0 is an even integer.

Hope it helps.

Hi! Why didn't we x=1 in the first case?

Posted from my mobile device

(1) says that (x+3) is a prime number. If x = 1, then x + 3 = 4, which is not a prime number.

I'm sorry. I meant why can't x =2

Then x+3 = 5
And s=1

In this case xs = 2*1 = even, which is exactly what we are getting in (1): for any value of x, satisfying the stem and the first statement, xs will be even,

Given: x and s are both positive integers.
Asked: Is the product of x and s even?

(1) (x+3) is a prime number
x=1, x+3=4 which is not prime
x=2, x+3=5 which is a prime number
x=4, x+3=7 which is a prime number
All prime numbers other than 2 are odd
x+3 is odd
x is even
The product of x with any positive integer s = even
SUFFICIENT

(2) (s+1) is a prime number
s=1, s+1=2 is a prime number
s=2, s+1=3 is a prime number
s=4, s+1=5 is a prime number
Since s=1 odd number satisfies the condition and all other s are even
NOT SUFFICIENT

IMO A

Solution

Given:

• x and s are positive integers

To find:

• x × s = Even?

o Product of two numbers is even is one of the numbers is even.
o Hence, we need to find whether x or s is even.

Analysing statement 1
“(x+3) is a prime number”

• x>= 1 as it is a positive integer.

o Hence, x+3 >=4
o And, prime number greater than 3 are always odd.
o x+3 = odd

 x = Even

• Since x is even, the product of x and s is even.

Hence, statement 1 is sufficient to find the answer.
Analysing statement 2
“(s+1) is a prime number”

• s>= 1 as it is a positive integer.

o Hence, s+1 >=2
o So, s+1 can be even or odd.
• Hence, s can be even or odd.

Thus, statement 2 is not sufficient to find the answer.

Hence, the correct answer is A.
Correct answer: Option A

Q: If x and s are both positive integers, is the product of x and s even?

1.(x+3) is a prime number

It given that x is a positive integer , i.e. x>0. That means x+3 > 3

So as per statement 1 , x + 3 is an odd prime no. If x + 3 is odd, then x should be even.

When you multiply an even number with any integer, the product should be always even.
So, we can conclude that the product of x and s is even.

Statement 1 alone is sufficient.

2. (s+1) is a prime number
S >0 as its given that S is positive integer. 0 is neither positive nor negative.
If S =1, S+1 = 1+1 = 2 is a prime no. In that case, S is odd. Therefore, the product of x and s can be odd or even depending on x.
So, Statement 2 alone is not sufficient.

Option A is the answer.

Thanks,
Clifin J Francis

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