hi karthikpandian19:

This is how I solved it
We have |b-2| + |b+8| , the concept to use with |X| questions is simple but important
1)if X<=0; |X| = -X
2)if X>=0; |X| = X

Now let's look at this one
1. b <=2 , then b-2<=0; if let's use b = -100, then |b-2| + |b+8| = |-100-2| + |-100+8| = 102 + 92 = 294, hence not sufficient

2. b>=-8 , then b+8>=0; let b = 100, again we see that |b-2| + |b-8| > 10; hence insufficient.
Let's look at both of them together,
we have b<=2, which implies b-2<=0; therefore |b-2| = -(b-2)
also we have, b>=-8 which implies b+8>=0; therefore |b+8| = (b+8)

Then we get |b-2| + |b-8| = -(b-2) + b+8 = -b + 2 + b + 8 = 10; hence C is the correct answer.

One can always use different cases for |x| questions and use the boldface expressions to solve almost all questions of this type.

1)if X<=0; |X| = -X
2)if X>=0; |X| = X

btw, karthikpandian19, you post really good questions

let me know if this helps

@eagleeye,

Basically you are letting me to know that we need to use Plugging In values over here along with the Boldface equations.
Nice explanation

eagleeye wrote:hi karthikpandian19:

This is how I solved it
We have |b-2| + |b+8| , the concept to use with |X| questions is simple but important
1)if X<=0; |X| = -X
2)if X>=0; |X| = X

Now let's look at this one
1. b <=2 , then b-2<=0; if let's use b = -100, then |b-2| + |b+8| = |-100-2| + |-100+8| = 102 + 92 = 294, hence not sufficient

2. b>=-8 , then b+8>=0; let b = 100, again we see that |b-2| + |b-8| > 10; hence insufficient.
Let's look at both of them together,
we have b<=2, which implies b-2<=0; therefore |b-2| = -(b-2)
also we have, b>=-8 which implies b+8>=0; therefore |b+8| = (b+8)

Then we get |b-2| + |b-8| = -(b-2) + b+8 = -b + 2 + b + 8 = 10; hence C is the correct answer.

One can always use different cases for |x| questions and use the boldface expressions to solve almost all questions of this type.

1)if X<=0; |X| = -X
2)if X>=0; |X| = X

btw, karthikpandian19, you post really good questions

let me know if this helps

yes, karthikpandian19, plugging in alongside algebra works well in these types. Once, we do more practice, the DS answers should become really fast.

Thanks for the kudos