If x and y are positive integers, is the product x

y even?

1)5x - 4y is even

2)6x + 7y is even

a)Exactly one of the statements can answer the question

b)Both statements are required to answer the question

c)Each statement can answer the question individually

d)More information is required as the information provided is insufficient to answer the question

Correct answer is option 'C'. Can you explain this answer?

Nonso Onyiagha
Jun 12, 2019 |

Even + Even = Even

Even - Even = Even

Even * Even = Even

Even * Odd = Even

Number 1 says 5x - 4y is even, according to the above stated rules, the 2 intergers involved must be even to give an even number, you can see that it is correct.

We can see that at least either x or y is even, and the product of an even number and an odd must give an even.

Also number 2 says the multiplication gives even.

The rules gives the answer, any one of the 2 options answers the question.

Even - Even = Even

Even * Even = Even

Even * Odd = Even

Number 1 says 5x - 4y is even, according to the above stated rules, the 2 intergers involved must be even to give an even number, you can see that it is correct.

We can see that at least either x or y is even, and the product of an even number and an odd must give an even.

Also number 2 says the multiplication gives even.

The rules gives the answer, any one of the 2 options answers the question.

Indu Bahl
Jan 31, 2020 |

1) 4y will always be even. Then we have 5x−even=even ,

For this to be the case, 5x must be even. Since 5 can't be even, then x must be even. Thus the product xy will be even. Sufficient.

2) 6x will always be even. Then we have even+7y=even.

2) 6x will always be even. Then we have even+7y=even.

Thus 7y is even, and y is even, and xy is even. Sufficient.

Even + Even = EvenEven - Even = EvenEven * Even = EvenEven * Odd = EvenNumber 1 says 5x - 4y is even, according to the above stated rules, the 2 intergers involved must be even to give an even number, you can see that it is correct.We can see that at least either x or y is even, and the product of an even number and an odd must give an even.Also number 2 says the multiplication gives even. The rules gives the answer, any one of the 2 options answers the question.