Tricky big book sum

Why is ans a ? Is it because values could be 2 and 8

or 3 an 7

or 4 and 6. So, we cannot find one fixed values of x and y. Is this the logic?

But am getting confused that we need to find values of x and y- values could be anything as long as those are values. a should be correct.

Yes

The question is asking you to determine a pair of numbers
With B, you know one of the numbers, you can subtract from the sum and find the other
With C, you will have 2 equations, x+y = known and xy = 8, through these the pair can be determined
Same with D and E

But with A, you have multiple possible pairs, so A will be the answer

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