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24 Sep 2020, 21:19
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Alternative approach:
x^2 =y^2 can be translated as x=y and x= -y
These lines are plot as seen red and blue respectively. The question stem asks if x>0
As of now it could be in any of the four quadrants
1. Statement 1 says: 2y+1=x
This is the black line. If you observe it intersects the above two lines at 2 points x= -1 and x= 1/3. Clearly we cannot say if x>0 . Therefore 1 alone is insufficient.
2. Statement 2 says: y<=1
This line also intersects the above 2 lines at 2 points. One at x<0 and other at x>0.
Statement 2 insufficient.
Combining 1 and 2, we can see that they all intersect only at x= -1
Therefore we can say that x<0.
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Picture1.png [ 52.7 KiB | Viewed 1473 times ]
x^2 =y^2 can be translated as x=y and x= -y
These lines are plot as seen red and blue respectively. The question stem asks if x>0
As of now it could be in any of the four quadrants
1. Statement 1 says: 2y+1=x
This is the black line. If you observe it intersects the above two lines at 2 points x= -1 and x= 1/3. Clearly we cannot say if x>0 . Therefore 1 alone is insufficient.
2. Statement 2 says: y<=1
This line also intersects the above 2 lines at 2 points. One at x<0 and other at x>0.
Statement 2 insufficient.
Combining 1 and 2, we can see that they all intersect only at x= -1
Therefore we can say that x<0.
24 Nov 2020, 14:29
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burnttwinky
\(x^2 - y^2 = 0\)
\((x+y)(x-y) = 0\)
\(x = -y\) or \(x = y\)
(1) \(x = 2y+1\)
\(y = 2y+1\)
\(y = -1 \)
or
\(-y = 2y+1\)
\(-3y = 1\)
\(y = \frac{-1}{3}\)
INSUFFICIENT.
(2) \(y ≤ -1\)
If \(x = y\), then \(x ≤ - 1\). However, if \(x = -y\), then \(x ≥ 1\). INSUFFICIENT.
(1&2)
\(2y ≤ - 2\)
\(2y + 1 ≤ -1\)
Therefore \(x ≤ -1\).
SUFFICIENT.
Answer is C.
16 Dec 2021, 02:15
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burnttwinky
x^2 = y^2
or |x| = |y|
means either x=y or x=-y
1) If x=y, then x=2x+1 or x=-1
If x=-y, then x=2(-x)+1 or x=1/3
Y/N depends on whether x=y or x=-y, we don't know (Insufficient)
2) It only tells us about the sign of y, can't deduce anything about x from this (Insufficient)
c) Combined x <= 2(-1)+1, we get x <= -1; sufficient
26 Feb 2025, 03:21
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