Power Prep -DS - Modulus

[thirst4edu]

If x & y are integers and y=|x+3| + |4-x|, does y equals 7?

1) x < 4
2) x > -3

Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks.

OA is C

[Rahul@gurome]

lx+3l = x+3 if x >= -3
= -(x+3) if x < -3.
l4-xl = 4 - x if 4-x > = 0 or if x <= 4.
= -(4-x) = x-4 if 4-x < 0 or if x > 4.

So Case (1) y = -(x+3) + (4 - x) = -2x + 1 if x < -3.
Case (2) y = (x+3) + (4-x) = 7 if -3 <= x <= 4.
Case (3) y = (x+3) + (x-4) = 2x -1 if x > 4.

Consider first (1) alone.
It says x < 4.
But we do not know whether x < - 3 or not.
Or (1) alone is not sufficient.

Next consider (2) alone.
It says x > -3 but do not know whether x > 4 or not.
So (2) alone is not sufficient.

Next combine both the statements together and check.
On combining we have that -3 < x < 4.
For this we have case (2) where y = 7 .
On combining we get a definite answer.

The correct answer is hence (C).

[thirst4edu]

lx+3l = x+3 if x >= -3
= -(x+3) if x < -3.
l4-xl = 4 - x if 4-x > = 0 or if x <= 4.
= -(4-x) = x-4 if 4-x < 0 or if x > 4.

So Case (1) y = -(x+3) + (4 - x) = -2x + 1 if x < -3.
Case (2) y = (x+3) + (4-x) = 7 if -3 <= x <= 4.
Case (3) y = (x+3) + (x-4) = 2x -1 if x > 4.

Consider first (1) alone.
It says x < 4.
But we do not know whether x < - 3 or not.
Or (1) alone is not sufficient.

Next consider (2) alone.
It says x > -3 but do not know whether x > 4 or not.
So (2) alone is not sufficient.

Next combine both the statements together and check.
On combining we have that -3 < x < 4.
For this we have case (2) where y = 7 .
On combining we get a definite answer.

The correct answer is hence (C).

Thanks Rahul!