Bunuel niks18 chetan2u pushpitkcQuote:
If |x| = |y| and xy = 0, which of the following must be true?
A \(xy^2>0\)
B. \(x^2y>0\)
C. \(x+y=0\)
D. \(\frac{x}{(y+1)}=2\)
E. \(\frac{1}{x}+\frac{1}{y}=\frac{1}{2}\)
Can you explain solving modulus on both sides of equality if it was a PS problem.
|x| = |y|
Do I definitely need to know if x or y is positive or negative?
I approached in below manner:
If product of two numbers x and y is zero, then EITHER of x or y is zero, or
BOTH x and y are zero.
With this logic, A,B and E are out. (Since this is PS problem ALL of above
conditions must be satisfied.)
For D, if x = 0 then RHS = 2 is Not satisfied, since LHS = 0
If y = 0 , then |0| = 0 LHS = 0/1 or 0, RHS = 2. Not satisfied.
Let me know if my steps are correct.
|x|=|y| implies magnitude of x and y are equal irrespective of their sign. For e.g. if x=2 and y=-2 then also |x|=|y|.
As you rightly mentioned xy =0 so either of the two has to be 0 but here as their magnitude are same so both x & y has to be 0