praetorian123 wrote:

Rules

1. Time yourself

2. Solve the problem seperately

3. Explain your solution and please mention your time.

Which of the following sets includes ALL of the solutions of x that will satisfy the equation:

|x тАУ 2| - |x тАУ 3| = |x тАУ 5|?

(A) {-6, -5, 0, 1, 7, 8}

(B) {-4, -2, 0, 10/3, 4, 5}

(C) {-4, 0, 1, 4, 5, 6}

(D) {-1, 10/3, 3, 5, 6, 8}

(E) {-2, -1, 1, 3, 4, 5}

Just a little twist

All the solutions to the equation are present in ONLY ONE of the answer choices.

Paul wins this one

Well, the reason other solutions were included was to force you guys to consider if there are any other solutions. If you understand absolute values perfectly, you should be able to solve ANY Gmat problem based on those concepts.

We may remove the absolute value if the signs of the expressions are the same

ok..lets see..for that, we need to look at intervals.

1. x<2

for all values x<2 , all the three "expressions" are negative.

so, we can remove the absolute value sign

|x тАУ 2| - |x тАУ 3| = |x тАУ 5|

x-2 - x+3 = x-5

x = 1+5 = 6 ;

Now this solution is not possible because we are looking solutions for x<2. so we need to discard this.

2. 2<x<3

For all values 2<x<3 , |x тАУ 2| is positive, but the other two are negative..

So, x- 2 + x-3 = -x+5 [ hope you see what i did here]

3x = 10

x=10/3

Again, 10/3 is not within range of our interval. so discard.

3. 3<x<5

For all values, 3<x<5, |x тАУ 2| and |x тАУ 3| are positive , but |x тАУ 5| is negative.

x-2 - x+3 = -x+5

x = 4 , ok 4 is within the interval ...so its one of our solutions.

4. x>5

Here all the expressions are positive. so, we can directly write

|x тАУ 2| - |x тАУ 3| = |x тАУ 5|

x-2 - x+3 = x-5

x = 1+5 = 6 ; Again, 6 is within the interval, so its our second and final solution.

Finally, our solutions are 4 and 6, which are both present ONLY in Choice C. Thus, C is our answer.