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gmatJP
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gmatJP
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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?
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nsp007
two unknowns, two equations

St. 1 : 4x+y=17 --> We cannot determine the value of either x or y. --> Insuff
St. 2 : x+4y=8 --> We cannot determine the value of either x or y. --> Insuff

St. 1 & 2 : 5x + 5y = 25 --> x+y = 5. Sufficient..hence, C.

Hope this helps !


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?
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nsp007
two unknowns, two equations

St. 1 : 4x+y=17 --> We cannot determine the value of either x or y. --> Insuff
St. 2 : x+4y=8 --> We cannot determine the value of either x or y. --> Insuff

St. 1 & 2 : 5x + 5y = 25 --> x+y = 5. Sufficient..hence, C.

Hope this helps !


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?

Yes, that's correct. You can sum two equations and then reduce.
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gmatJP
Does x + y = 5 ?

(1) 4x + y = 17
(2) x + 4y = 8

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
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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.)
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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.)

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
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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.
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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) ?
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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) ?

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.
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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
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