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11 Jul 2019, 01:34
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11 Jul 2019, 01:51
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Bunuel
Does x – y = 0 ?
(1) x/y > 0
(2) x^2 = y^2
(1) x/y > 0
(2) x^2 = y^2
Q: is x=y?
S1:
x/y>0
=> (x>0 & y>0) or (x<0 & y<0)
=> x & y both have same sign (+ve or -ve)
x=3 & y=4 => x<>Y
x=3 & y=3 => x=y
NOT SUFFICIENT
S2:
x^2 = y^2
|x| = |y|
x & y may have different sign (+ve or -ve)
NOT SUFFICIENT
S1 & S2:
S1: x & y both have same sign (+ve or -ve)
S2: |x| = |y| => x & y have same magnitude
Since x & y have same sign and same magnitude
=> x & y are same
=> x =y
SUFFICIENT
IMO C
RawJoker
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13 Feb 2020, 09:27
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The question is asking whether, X = Y ?
Option 1: x/y > 0
Taking values,
(1) x = 3, y = 2...We get x/y >0. Checking back with main question we get x <> y.
(2) x = 2, y = 2...We still get x/y >0. However, in this case we get x = y.
Hence, Option (1) itself is Not Sufficient.
Option 2: x^2 = y^2
Taking values,
(1) x = -2, y = 2...We get x^2 = y^2. Checking back with main question we get x <> y.
(2) x = 2, y = 2...We still x^2 = y^2. However, in this case we get x = y.
Hence, Option (2) itself is Not Sufficient.
Taking Option (1) and Option (2) together,
x^2 = y^2, will only be possible when the absolute value of x and y are the same, i.e. |x| = |y|
Also, from Option (1), we know x/y > 0, meaning x and y will be of the same sign. If they would be of different signs, then the value would have been negative, which is not the case as per, x/y > 0.
Taking values,
(a) x = 2, y = 2...We get x^2 = y^2 and also x/y > 0. Checking back with main question we get x = y.
(2) x = -2, y = -2...We again get x^2 = y^2 and also x/y > 0. Again, we get x = y.
Therefore, from Option (1) and Option (2) we can clearly say x = y.
Hence, Option (3), both together, is sufficient to solve the question.
Option 1: x/y > 0
Taking values,
(1) x = 3, y = 2...We get x/y >0. Checking back with main question we get x <> y.
(2) x = 2, y = 2...We still get x/y >0. However, in this case we get x = y.
Hence, Option (1) itself is Not Sufficient.
Option 2: x^2 = y^2
Taking values,
(1) x = -2, y = 2...We get x^2 = y^2. Checking back with main question we get x <> y.
(2) x = 2, y = 2...We still x^2 = y^2. However, in this case we get x = y.
Hence, Option (2) itself is Not Sufficient.
Taking Option (1) and Option (2) together,
x^2 = y^2, will only be possible when the absolute value of x and y are the same, i.e. |x| = |y|
Also, from Option (1), we know x/y > 0, meaning x and y will be of the same sign. If they would be of different signs, then the value would have been negative, which is not the case as per, x/y > 0.
Taking values,
(a) x = 2, y = 2...We get x^2 = y^2 and also x/y > 0. Checking back with main question we get x = y.
(2) x = -2, y = -2...We again get x^2 = y^2 and also x/y > 0. Again, we get x = y.
Therefore, from Option (1) and Option (2) we can clearly say x = y.
Hence, Option (3), both together, is sufficient to solve the question.
