Let x = 11 and y = 7,

2xy = (2)(11)(7) = 154

x + 2y = 11+ (2)(7) = 25

xy = (11)(7) = 77

x - y = 11-7 = 4

2^y = 2^7 = 128

From this I can infer every options are not a prime number. Confused…

Let x = 11 and y = 7,

2xy = (2)(11)(7) = 154

x + 2y = 11+ (2)(7) = 25

xy = (11)(7) = 77

x - y = 11-7 = 4

2^y = 2^7 = 128

From this I can infer every options are not a prime number. Confused…

I agree with you here

Hint: cannot.

Is it **always** true that given x and y are prime numbers, the given options cannot be prime numbers (no matter what they are)? x = 11 and y = 7 is just one example.

For example, if x = 3 and y = 2, x + 2y = 7, which **is** prime.

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So basically, the question wants us to choose answer which is guaranteed to give a non-prime numbers. Wrong options could give a prime number hence they are wrong. Am I right?

Correct.

So I need to check with another set of numbers before confirming?

That would help; alternatively you can take a conceptual angle to find out which options **must** be correct. For example, A and C can never be prime since xy and 2xy must mean that you have at least three factors.

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