Countdown wrote:

Please help regarding the below question wid explanation.

If a , b, and c are integers and ab2 / c is a positive even integer, which of the following must be true?

I. ab is even II. ab > 0 III. c is even

I only

II only

I and II

I and III

I, II, and III

I believe the expression is \(ab^2/c\) is a positive integer.

Now we know,

1. even * even = even (2*4 = 8)

2. even * odd = even (2*3 = 6)

3. even / even = even or odd (8/2 = 4 , 6/2 = 3)

4. even / odd = even (6/3 = 2)

5. odd * odd = odd

6. odd / odd = odd (if the are divisible)

7. odd / even = <not divisible> as the denominator will always have an extra 2.

Coming back to my question, my result is even. Hence my numerator must be even, as odd numerator can never give even result. (we are considering divisible integers only)

\(ab^2\) is even, hence either a is even or \(b^2\) is even. If \(b^2\) is even then b is even. Hence ab = even. (I) is true.

now \(\sqrt{b^2}\) = +/- b, so ab can be > 0 or < 0, (II) is false

From rule 3 and 4, c can be even or odd. so (III) is false.

Answer A.

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Thanks!