VeritasPrepKarishma wrote:
Hussain15 wrote:
If x + |x| + y = 7 and x + |y| - y =6 , then x + y =
A. 3
B. 4
C. 5
D. 6
E. 9
In such a question, you can use some brute force and get to the answer too. How long it takes depends on how quickly you observe the little things.
x + |x| + y = 7
x + |y| - y =6
Both equations yield about the same result though in one y is positive and in the other it is negative. |x| and |y| are positive and assuming x is positive, a negative y would pull down the first equation and pump up the second one to give almost equal values. The difference is very small also signifies that the negative variable might have a very small value.
Since the options give the value of x + y as 3/4/5... etc, it is likely that we are dealing with small number pairs such as (4, 2), (3, 2), (4, 1) etc.
Since the first equation has 7 as the result, both variables will not be even.
A couple of quick iterations brought me to (4, -1).
So x + y = 3
Hi Karishma,
I tried another approach, but got stuck - can you hep me solve by this method?
x + |x| + y = 7 => x + y = 7 - |x| => Whatever be the value of x, |x| will be always non-negative => x + y has to be less than 7 => This eliminates option E
x + |y| - y = 6 => Now, if y is positive, then this equation becomes x = 6 => on substituting in above eqn, we get y = -5 => x+y = 1 => Not present in any of the options => y is negative => x - y - y = 6 => x - 2y = 6 => x = 6 + 2y
Now x + y = 7 - |6 + 2y|
If we take y = -1, we get x + y = 3 = Option A
If we take y = -2, we get x + y = 5 = Option C
I am getting both options here - where am I going wrong here? Or this approach incorrect?