modulus

[vishal.pathak]

|x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2
OA not available

Is |x+y|>|x-y|?
(1) |x| > |y|
(2) |x-y| < |x|
OA not available

[Bill@VeritasPrep]

|x+2|=|y+2| what is the value of x+y?

(1) xy<0
If the product is negative, then one of our variables is positive and the other is negative. If x=4, then y=-8. 4 + -8= -4. If x=-8, then y=4. -8 + 4 = -4. Sufficient since we get the same value each time.

(2) x>2 y<2

Our first example from statement 1 meets these requirements, so we can reuse it. If x=4, then y=-8. 4 + -8 = -4. If x =8, then y = -12. 8 + -12 = -4. Sufficient since we get the same value each time.

The correct answer is D.


Is |x+y|>|x-y|?

(1) |x| > |y|

If x=6 and y=4, then abs(6+4)=10 and abs(6-4)=2. YES
If x=2 and y=0, then abs(2+0)=2 and abs(2-0)=2. NO

Insufficient

(2) |x-y| < |x|

Our first example from statement 1 still holds: abs(6-4)=2, abs(6)=6
If x=6 and y=4, then abs(6+4)=10 and abs(6-4)=2. YES

If x=-4 y =-2, abs(-4 - -2) = 2, abs(-4)=4
abs(-4 + -2)=6, abs(-4 - -2) = 2. YES

Essentially, Statement 2 rules out the possibility that y=0 (which is what made the first statement insufficient), which allows us to answer with a definitive yes. Sufficient, so the correct answer is B.

Bill

[vishal.pathak]

|x+2|=|y+2| what is the value of x+y?

(1) xy<0
If the product is negative, then one of our variables is positive and the other is negative. If x=4, then y=-8. 4 + -8= -4. If x=-8, then y=4. -8 + 4 = -4. Sufficient since we get the same value each time.

(2) x>2 y<2

Our first example from statement 1 meets these requirements, so we can reuse it. If x=4, then y=-8. 4 + -8 = -4. If x =8, then y = -12. 8 + -12 = -4. Sufficient since we get the same value each time.

The correct answer is D.


Is |x+y|>|x-y|?

(1) |x| > |y|

If x=6 and y=4, then abs(6+4)=10 and abs(6-4)=2. YES
If x=2 and y=0, then abs(2+0)=2 and abs(2-0)=2. NO

Insufficient

(2) |x-y| < |x|

Our first example from statement 1 still holds: abs(6-4)=2, abs(6)=6
If x=6 and y=4, then abs(6+4)=10 and abs(6-4)=2. YES

If x=-4 y =-2, abs(-4 - -2) = 2, abs(-4)=4
abs(-4 + -2)=6, abs(-4 - -2) = 2. YES

Essentially, Statement 2 rules out the possibility that y=0 (which is what made the first statement insufficient), which allows us to answer with a definitive yes. Sufficient, so the correct answer is B.

Bill

Hi Bill,

Many thanks for your kind response.

My motive of posting these 2 questions was the understand the method of forming various regions for these kind of equations
For example: The regions of |x + 1| + |x - 3| = 6 are x < -1, -1 < x < 3, and x > 3.

How can we form the regions for the above 2 questions?

Regards,
Vishal