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

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

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New post 26 Nov 2017, 22:27
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Re: Are x and y both negative? (1) 3x - 3y = 1 (2) x/y < 1 [#permalink]

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New post 26 Nov 2017, 22:28

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Re: Are x and y both negative? (1) 3x - 3y = 1 (2) x/y < 1 [#permalink]

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New post 26 Nov 2017, 22:43
Bunuel wrote:
Are x and y both negative numbers?

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


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.

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Re: Are x and y both negative? (1) 3x - 3y = 1 (2) x/y < 1 [#permalink]

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New post 27 Nov 2017, 00:20
(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

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

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New post 28 Nov 2017, 15:54
Bunuel wrote:
Are x and y both negative numbers?

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


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,

Last edited by rulingbear on 29 Nov 2017, 12:30, edited 2 times in total.

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Re: Are x and y both negative? (1) 3x - 3y = 1 (2) x/y < 1 [#permalink]

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New post 28 Nov 2017, 22:24
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(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

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Re: Are x and y both negative? (1) 3x - 3y = 1 (2) x/y < 1   [#permalink] 28 Nov 2017, 22:24
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