Question: Is 10mn + 7 odd?

Question

Is 10mn + 7 odd?

I'm just wondering if my answer is alright.

Suppose 10mn [particular but arbitrarily chosen] is an even integer. [We must show that 10mn + 7 is odd]. By definition of even, m=2r and n=2s for some integers r and s. Then

10mn + 7 = 10(2r)(2s) + 7 (by substitution)

= 40rs + 7

= 2(20rs) + 7

Now let k = 20rs. By definition of even, 10mn is even since 10mn = 2k.

Now 10mn + 7 = 3k + 7 (where k is the products of integers)

It follows by definition of odd that 10mn + 7 is odd.

I think i messed up the 2nd half of it. Can someone please kindly correct this for me. I'm quite lousy at proving things.

Thank you :)

Answer 1

10mn is always even

7 is odd

the sum of an odd and an even number will always be odd.  

Answer 2

idk

Answer 3

if m and n are integers then 10mn will always end with a 0 so when you add 7 to it, last digit will be 7. Hence odd.

Answer 4

Yes:

10mn + 7 IS odd because:

Anything multiplied by 10 is even (it's divisble by 2). Think of it as:

10(mn)

Now, add 7 and that will make it odd (even + odd = odd)

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Your proof is right but just a little error:

2(20rs) + 7

Letting k = 20rs

2k + 7

You put down 3k