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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
56% (01:10) correct
44%
(01:38)
wrong
based on 268
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What is the value of x - y?
(1) \(x^3 - y^3 = 0\\
\)
(2) \(x^4 - y^4 = 0\)
(1) \(x^3 - y^3 = 0\\
\)
(2) \(x^4 - y^4 = 0\)
17 Aug 2022, 22:07
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statement 1:
x^3-y^3= 0
=> x^3=y^3
=> x= y ( odd power represents same sign, same magnitude )
sufficient
statement 2:
x^4-y^4=0
=>x^4=y^4
now the sign of x and y can be same or different. no definite ans
not sufficient
IMO A
x^3-y^3= 0
=> x^3=y^3
=> x= y ( odd power represents same sign, same magnitude )
sufficient
statement 2:
x^4-y^4=0
=>x^4=y^4
now the sign of x and y can be same or different. no definite ans
not sufficient
IMO A
18 Aug 2022, 02:18
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(1) x^3−y^3=0
Since x^3 will have the same sign as x and y^3 will have the same sign as y
In this scenario, x has to be equal to y and x and y would have similar signs
Expanding x^3−y^3 we get
(x-y)(x^2 + xy + y^2) = 0
So either x - y = 0
Or x^2 + xy + y^2 = 0
Since x and y cannot have opposite signs, the above expression will always be positive except if x = y = 0
Hence x - y = 0
--> Sufficient
(2) x^4−y^4=0
Here we know that |x| = |y| but x may or may not be equal to y
Example
1) x = 2 and y = 2 Satisfies
2) x = 2 and y = -2 Does not satisfy
Two different answers
--> Insufficient
Option A
Since x^3 will have the same sign as x and y^3 will have the same sign as y
In this scenario, x has to be equal to y and x and y would have similar signs
Expanding x^3−y^3 we get
(x-y)(x^2 + xy + y^2) = 0
So either x - y = 0
Or x^2 + xy + y^2 = 0
Since x and y cannot have opposite signs, the above expression will always be positive except if x = y = 0
Hence x - y = 0
--> Sufficient
(2) x^4−y^4=0
Here we know that |x| = |y| but x may or may not be equal to y
Example
1) x = 2 and y = 2 Satisfies
2) x = 2 and y = -2 Does not satisfy
Two different answers
--> Insufficient
Option A
