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If x and y are integers, what is the value of x?
(1) The sum of the squares of x and y is equal to the square of their sum.
(2) The product of x and y is less than their sum.
(1) The sum of the squares of x and y is equal to the square of their sum.
(2) The product of x and y is less than their sum.
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14 Jun 2017, 04:20
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Bunuel
If x and y are integers, what is the value of x?
(1) The sum of the squares of x and y is equal to the square of their sum.
(2) The product of x and y is less than their sum.
(1) The sum of the squares of x and y is equal to the square of their sum.
(2) The product of x and y is less than their sum.
(1) gives us X^2 + Y^2 = (X+Y)^2
hence XY = 0 where either X can be 0 or Y can be 0 hence insufficient
(2) XY< X+Y
X>XY-Y
X>Y(X-1)
Not Sufficient
On combining both we get X+Y>0
If X=0 then Y is +integer which cannot be possible as it does not hold X> Y(X-1)
if Y=0 then X is a +ve integer and holds X>Y(X-1)
However then also we will not be able to identify the value of X
Hence E
Please correct me if i am wrong
Heisenberg12
15 Jun 2017, 04:11
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X and Y are integers.
1) X^2 + Y^2 = (X+Y)^2
This implies 2XY=0, hence, either X=0 or Y=0, thus this statement is insufficient.
2) XY < (X+Y), thus either X or Y could be 0 or 1, but we can't be sure of it. Hence, it is insufficient by itself.
Combining both, we still could not tell what could be the value of X. X could be any integer other than 0, with condition that Y is 0. Similarly, X could be 0 and Y could be any integer other than 0. This is still insufficient.
Hence, E.
1) X^2 + Y^2 = (X+Y)^2
This implies 2XY=0, hence, either X=0 or Y=0, thus this statement is insufficient.
2) XY < (X+Y), thus either X or Y could be 0 or 1, but we can't be sure of it. Hence, it is insufficient by itself.
Combining both, we still could not tell what could be the value of X. X could be any integer other than 0, with condition that Y is 0. Similarly, X could be 0 and Y could be any integer other than 0. This is still insufficient.
Hence, E.
