Does x + y = 5 ? (1) 4x + y = 17 (2) x + 4y = 8

Yes, that's correct. You can sum two equations and then reduce.

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.

But I can still solve following way;

x+y=5 so x=5-y or y=5-x

1) 4x+y=17 --- y=17-4x
so insert this into givin equ, x=5-17+4x --- x-4x=-12 is x=4
also y=5-4=1 x+y=5 Sufficient

same concept with 2)

As this way the answer becomes D but why not this way??

we have two equation when 1) is givin.
Am I missing something?

Given : nothing
DS : x+y = 5?

Statement 1 : 4x + y = 17 (2 variables, one equation. Also can't be reduced to shortest form)
NOT SUFFICIENT

Statement 2: x + 4y = 8 (2 variables, one equation. Also can't be reduced to shortest form)
NOT SUFFICIENT

Combined : Add both equations
5 (x+y ) = 25
-> x+y = 5
SUFFICIENT

Answer C

Hello

You are probably doing like this:

(1) 4x+y = 17
Taking it along with data in the question x+y = 5; we have two unknowns and two equations - so we can solve, we can find x and y, and thus determine whether x+y = 5 or not.

(2) Same logic in statement 2.


I think thats how you are getting your answer as D.

But the thing is - we cannot take the data x+y =5 to be true, because that is what we have to determine whether is true or not in the first place

If (2) were x + 4y = 9 instead of x + 4y = 8 the answer would still be C. (2) would not be sufficient, because if x = 11/3 and y = 4/3, then the answer would be YES (x + y = 5) but if x = 1 and y = 2, the answer would be NO (x + y ≠ 5). However, when combining we could find the values of x and y (x = 59/15 and y = 19/15 satisfy x + 4y = 9 and 4x + y = 17) and answer the question whether x + y = 5. The answer in this case would be NO: x + y ≠ 5.

Hope it's clear.

This is hoe I came about the problem as well! But this looks very simple.

So I wonder, is this the right way to solve the above problem?

Bunuel, can you let me know if this is the right way to solve the above problem?

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.)

If for example in the second statement: instead of x+4y=8, we have x+4y=9.
If we try for x and y, there's no two possible values of x and y that add to 5. so x+y can never be 5. Will the statement be sufficient (always no) ?

I have a problem trying to eliminate D, can someone tell my what I am doing wrong?

(1) 4x + y = 17

So x + y = 17/4 I can determine that it is not 5, sufficient

(2) 2x + 4y = 8

Same here, x + y = 8/2 so it is not 5