aaronhew
I understand that C is a correct. It's just confusing to me as to why D is incorrect when both statements (taken individually) along with the given information is sufficient to determining whether x + y = 5. So, I'm having a hard time eliminating D as an incorrect answer choice. Perhaps I'm comprehending the question incorrectly.
Can someone please explain to me why D is the incorrect answer?
(let me know if my question is unclear.)
Does x + y = 5 ?(1) 4x + y = 17. Infinitely many value of x and y satisfy this equation, and only one pair of (x,y), will x + y equal to 5, namely x = 4 and y = 1. For all other values x + 5 won't be 5. For example, if x = 1 and y = 13, then x + y is 14, not 5. We have both YES and NO answer to the question, so this statement is not sufficient.
(2) x + 4y = 8. The same here. Infinitely many value of x and y satisfy this equation, and only one pair of (x,y), will x + y equal to 5, namely x = 4 and y = 1. For all other values x + 5 won't be 5. For example, if x = 0 and y = 2, then x + y is 2, not 5. We have both YES and NO answer to the question, so this statement is not sufficient.
(1)+(2) Now, we have two distinct linear equations: 4x + y = 17 and x + 4y = 8. We can solve and get exact value of x and y and thus answer the question whether x + y = 5. Though, it's not necessary to actually solve but just to demonstrate, solving gives x = 4 and y = 1. For these values x + y = 5. So, we have a definite YES answer to the question. Sufficient.
Answer: C.
Hope it helps.