Are x and y both negative? (1) 3x - 3y = 1 (2) x/y

Question

Are x and y both negative numbers?

(1) 3x - 3y = 1 
(2) x/y < 1

Bunuel · Answer

Similar question from GMAT Prep: https://gmatclub.com/forum/are-x-and-y- ... 63377.html

rahul16singh28 · Answer

Hi  Bunuel

Stmnt 1: x - y= 1/3.. Not Sufficient.
Stmnt 2: y-x/y > 0.. Not Sufficient..

1 +2.. (-1/3)/y > 0.. which means y = -ve number
x = y + 0.33.. Here, x can be both +ve and -ve.

Cab you please let me know if there is anything wrong with the approach.

Alexey1989x · Answer

(1) 3x-3y=1
x-y=1/3
case 1, both x and y are -ve:
x-y=-8/3-(-9/3)=1/3
case 2, = x and y are +ve:
x-y=3-8/3=1/3

Insufficient

(2) from this statement we understand, that |x|<|y|
(1) + (2) 
Combining, we eliminate case 2 from reasoning in (1) statement taken the condition in (2), so we get that both statements are valid only when x and y take -ve values 
Answer C

rulingbear · Answer

Statement 1 tells us  x > y  by  \frac{1}{3} 
Insufficient, as  x  and  y  could be any sign.

Statement 2 tells us  \frac{x}{y}  is less than one. Again just the same info in statement 1  (x>y) , except not as exact. Insufficient.

Now let's step back and consider both equations together. One or both variables have to be negative given both statements. Since we have 2 different cases with the same result, then neither statement is sufficient.  Hence E .

While there are infinite numerical examples,  -1  and  \frac{-2}{3}  or  \frac{1}{6}and \frac{-1}{6}  are prime examples.

CASE 1  (\frac{-2}{3}, -1)

\frac{-2}{3} - (-1)  =  \frac{1}{3} ... (1)

\frac{2}{3}  is absolutely less than  1 .... (2)

CASE 2  (\frac{1}{6}, \frac{-1}{6})

\frac{1}{6} - (\frac{-1}{6})  =  \frac{1}{3} ... (1)
 \frac{x}{y} = -1   <1 ... (2)

Since both variables could negative or one could, then the answer is E.

Note that I wrongly assumed that the one negative and positive coordinates (case 2) won't make a difference and the answer should be C. However, amanvamagmat below called my attention to this error in his post.

Best,

amanvermagmat · Answer

(1) 3x-3y=1 or x-y = 1/3. This just tells us that x>y, we dont know about their signs. Both could be positive, both could be negative, or we can have x positive, y negative. Insufficient.

(2) x/y < 1. Again we cant say about the signs.
Both x&y could be positive, in which case: x<y
Both x&y could be negative, in which case: x>y
One out of x&y could be positive, and other negative; in which case x/y will be negative and hence < 1
Insufficient.

Combining the two statements,
Both x&y cannot be positive, because in that case x-y=1/3 and x/y < 1 both cannot be true
Both x&y CAN be negative, eg; x=-1, y=-4/3. In this case: x-y = 1/3 and x/y < 1
We CAN also have x positive, y negative, eg: x=1/6, y=-1/6. In this case: x-y = 1/3 and x/y < 1

So there is no surety whether both x&y are negative or only one out of them is negative. Insufficient. Hence E answer

Are x and y both negative? (1) 3x - 3y = 1 (2) x/y < 1

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