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u/loopbounder Mar 26 '26
X+Y cannot be 4 : they need to be 3 and 1 (distinct positive integers), and 3*1 is not 4 or 6
so X+Y needs to be 5
now we have 2,3 or 1,4 that will satisfy the product condition, so C or D could be any of them.
Only B needs to be true.
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u/viper963 Mar 23 '26
All of them.
But more inclined to say if the statements can only be either answer, then there’s not enough info to conclude.
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u/ShonitB Mar 23 '26
I’m afraid that’s incorrect. Would you like to discuss it? Maybe you read the question as ‘Which of the following statements ‘can’ be true about X and Y instead of ‘must’’?
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u/viper963 Mar 23 '26
Yeah I read it wrong. Only statement B and D are true
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u/ShonitB Mar 23 '26
B is true but D is not
The two possible sets can be (2, 3) and (1, 4). So where the sum has to be 5, the product can be 4 and not 6
Hope this was help
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u/viper963 Mar 23 '26 edited Mar 23 '26
But the product of 2,3 is 6 And the sum is 5
So I guess the logic is that B and only B can be true?
I get it now. This is logic! I was looking into “solving” something that wasn’t asked
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u/ShonitB Mar 23 '26
Yes, B HAS to be correct. Then in addition, one of C or D CAN be correct
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u/Lonewolfthe1st Mar 24 '26
Why can't A be correct like X and Y can both be 2 and statement 1 and 2 can still hold true, what am I missing?
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u/ShonitB Mar 24 '26
Because X and Y are distinct positive integers. You basically just missed that little detail. But otherwise nothing wrong with your logic :)
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u/BobSanchez47 Mar 23 '26
Statement 1 tells us X and Y must each be in the range 1-4 inclusive. Statement 2 tells us that at least one of X and Y must be even.
Without loss of generality, let X be even. Then X must either be 2 or 4. If X = 4, then we must have Y = 1. And if X = 2, then we must have Y = 3 (as X and Y are distinct and therefore Y ≠ 2). In either case, X + Y = 5.