x is a positive integer greater than 2; is (x^3 + 19837) (x^2 + 5) (x - 3) an odd number?
[1] The sum of any prime factor of x and x is even.
[2] 3 x is an even number.
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(x^3 + 19837) (x^2 + 5) (x – 3) an odd
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- sanju09
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If x is even, then x^3 and x^2 are even too,
then (x^3 + 19837), (x^2 + 5), and (x - 3) are odd.
then the product will be odd.
If x is odd, then x^3 and x^2 are odd too,
then (x^3 + 19837), (x^2 + 5), and (x - 3) are even.
then the product will be even.
Thus if we can define whether x is an even or odd, we can define the property of the product.
1. All prime numbers are odd, except 2. Thus prime numbers can be odd or even
So we cannot define whether x is even or odd.
INSUF.
2. 3x is an even, then x is an even. As even divided by an odd, if divisible, will give out an even.
Now we know that x is even, then the product must be odd.
SUFF.
Pick B.
then (x^3 + 19837), (x^2 + 5), and (x - 3) are odd.
then the product will be odd.
If x is odd, then x^3 and x^2 are odd too,
then (x^3 + 19837), (x^2 + 5), and (x - 3) are even.
then the product will be even.
Thus if we can define whether x is an even or odd, we can define the property of the product.
1. All prime numbers are odd, except 2. Thus prime numbers can be odd or even
So we cannot define whether x is even or odd.
INSUF.
2. 3x is an even, then x is an even. As even divided by an odd, if divisible, will give out an even.
Now we know that x is even, then the product must be odd.
SUFF.
Pick B.
"There is nothing either good or bad - but thinking makes it so" - Shakespeare.
- limestone
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For 1.
Let's say x = 8
Prime factor of x: 2
The sum of x and its prime factor : 2+8 = 10 is an even
Let's say x = 9
Prime factor of x: 3
The sum of x and its prime factor : 3+9 = 12 is an even too
So with the given information that the sum of x and its prime factor is even, x can be either odd or even.
The the product : (x^3 + 19837) (x^2 + 5) (x - 3) can be either odd or even too.
Then 1 is INSUFF.
Let's say x = 8
Prime factor of x: 2
The sum of x and its prime factor : 2+8 = 10 is an even
Let's say x = 9
Prime factor of x: 3
The sum of x and its prime factor : 3+9 = 12 is an even too
So with the given information that the sum of x and its prime factor is even, x can be either odd or even.
The the product : (x^3 + 19837) (x^2 + 5) (x - 3) can be either odd or even too.
Then 1 is INSUFF.
"There is nothing either good or bad - but thinking makes it so" - Shakespeare.
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Correct - but it doesn't say that all of the prime factors of x are greater than 2. So, from (1) x could be either even or odd.ankurmit wrote:Its mentioned that X is geater than 2
x is a positive integer greater than 2; is (x^3 + 19837) (x^2 + 5) (x - 3) an odd number?
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