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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:24) correct
33%
(01:32)
wrong
based on 97
sessions
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Is \(x > y\)?
(1) \(x + y > 0\)
(2) \(y^2 > x^2\)
(1) \(x + y > 0\)
(2) \(y^2 > x^2\)
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06 Jun 2022, 08:44
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Bunuel
Is \(x > y\)?
(1) \(x + y > 0\)
(2) \(y^2 > x^2\)
(1) \(x + y > 0\)
(2) \(y^2 > x^2\)
target is x>y or say is x-y>0
#1
x+y>0
possible cases x,y ( 2,1) or (1,2)
insufficient
#2
y^2>x^2
possible cases x,y ( -1,-2) ; ( 1,2) ; (1,-2)
insufficient
from 1&2
we can say we have following cases
case 1 : both are +ve such that y>x
case 2: x is -ve & y is +ve such that y>x
we get no to target
option C sufficient
25 Sep 2022, 12:18
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Question
Before we proceed to the options, lets translate the question.
x > y ?
Inference : Does x lie to the right of y in a number line ?
Statement 1
x + y > 0
We know that the sum of x and y lie to the right of 0 in the number line, however we do not know the position of x or y relative to each other.
x may lie to the right of y or to the left of y and this statement alone does not give us any valuable information to conclude.
Hence this statement is not sufficient.
Statement 2
\(x^2 > y^2\)
\(x^2 - y^2 > 0\)
(x+y)(x-y) > 0
Plotting on a number line we know that y lies between x and -x as shown below.
Screenshot 2022-09-26 004521.png [ 20 KiB | Viewed 1280 times ]
However, we do not know the nature of x to conclude anything further.
If x is +ve : y lies to the left of x
If x is -ve : y lies to the right of x
Hence this statement is also not sufficient on its own.
Combining
However, when we combine both the statements
We know x + y > 0, so if x is negative as y can never exceed -x the sum will be negative and this case is no longer valid.
Hence x has to be positive and y will lie to the left of x.
Combined we have sufficient information to answer the question.
Option C
Before we proceed to the options, lets translate the question.
x > y ?
Inference : Does x lie to the right of y in a number line ?
Statement 1
x + y > 0
We know that the sum of x and y lie to the right of 0 in the number line, however we do not know the position of x or y relative to each other.
x may lie to the right of y or to the left of y and this statement alone does not give us any valuable information to conclude.
Hence this statement is not sufficient.
Statement 2
\(x^2 > y^2\)
\(x^2 - y^2 > 0\)
(x+y)(x-y) > 0
Plotting on a number line we know that y lies between x and -x as shown below.
Attachment:
Screenshot 2022-09-26 004521.png [ 20 KiB | Viewed 1280 times ]
However, we do not know the nature of x to conclude anything further.
If x is +ve : y lies to the left of x
If x is -ve : y lies to the right of x
Hence this statement is also not sufficient on its own.
Combining
However, when we combine both the statements
We know x + y > 0, so if x is negative as y can never exceed -x the sum will be negative and this case is no longer valid.
Hence x has to be positive and y will lie to the left of x.
Combined we have sufficient information to answer the question.
Option C
