mgmat ds - Absolutes and inequalities

is it C)?

as you can see from the roots of the absolute term

we need both statement..Choose C

Stmt I

x=-10 NO
x-0 yes

INSUFF

Stmt II
x=10 no
x= 0 yes

INSUFF

Stmt I and II together

-7<x<2 All values lead to y = 9

SUFF

Choose C)

Guys/Gals algebric approach welcome!

Acecollan,
Does Manhattan provide an algebric approach or is it also picking numbers strategy?

acecoolan wrote:q. If y = |x + 7| + |2 - x|, is y = 9?

(1) x < 2
(2) x > -7

Algebra in the house:

Statement 1)

x<2

|2 - x| = 2-x

|x + 7| = x+7 , when -7<x<2

|x + 7| = -x-7 when -7<x

so Y can be 9 between -7<x<2

but -2x-5 when X < -7

INSUF

Statement 2

almost same logic

ST1+ST2

Y can be 9 between -7<x<2

Bingo!

logitech wrote:

acecoolan wrote:q. If y = |x + 7| + |2 - x|, is y = 9?

(1) x < 2
(2) x > -7

Algebra in the house:

Statement 1)

x<2

|2 - x| = 2-x

|x + 7| = x+7 , when -7<x<2

|x + 7| = -x-7 when -7<x

so Y can be 9 between -7<x<2

but -2x-5 when X < -7

INSUF

Statement 2

almost same logic

ST1+ST2

Y can be 9 between -7<x<2

Bingo!

Wow ..great solutions. I wish I was half as good as u dealing with inequalities.

The ans is C) - thanks logitech and ramya

acecoolan wrote:[

Wow ..great solutions. I wish I was half as good as u dealing with inequalities.

The ans is C) - thanks logitech and ramya

My friend,

Keep posting question types that you are having problem with and we can try our best to help you. We are all here for one reason:

To learn from each other.

cramya wrote: Does Manhattan provide an algebric approach or is it also picking numbers strategy?

They have a highly conceptual approach ....almost put me to sleep ..
it goes like this ....

This question could be solved using a systematic algebraic approach. It would start like this: the two absolute value expressions each have two scenarios that must be considered. If we consider the intersection of these four scenarios, we will come up with three different equations (Theoretically there should be four different equations given the two scenarios for each expression, however, one of the equations would never hold since x cannot be both less than -7 and greater than 2). The process of considering these three different equations would be quite tedious and time consuming.

If we apply a conceptual understanding of absolute values, we can greatly simplify the solution to this problem. As we learned earlier in the series, each absolute value expression has two scenarios, a positive and a negative one. Recall that these scenarios are true for a given range of values. For example, the first expression /x + 7/ has two scenarios: one when x is greater than -7 and one when x is less than -7. -7 is called the critical point of this absolute value expression. What is the critical point of the second absolute value expression in the above equation? 2. Notice that the critical point is the value of x that would cause the absolute value expression to be zero.

Now that we have the critical points of the two absolute value expressions in this equation, we are poised for a strategic, conceptual solution to this question. Because there are two critical points, the equation y = /x + 7/ + /2 - x/ will have three different forms, one for each of three critical regions: x < -7, -7 < x < 2, and x > 2.

The question asks us if this equation can be simplified to y = 9. Let's look at the statements. Statement (1) says that x < 2. Is y = 9 for all x's less than 2? If we plugged a few values for x less than 2, i.e. x = 1, 0, -1, we might come to the hasty decision that in fact y is always equal to 9 when x < 2. The problem with this set of numbers, however, is that it doesn't do justice to the critical regions in the problem. For statement (1) we must check values not only less than 2 but also less than -7. Otherwise we are artificially restricting the statement to one of the three critical ranges for the problem. In fact when we check x = -10, we see that y is not equal to 9, so statement (1) is not sufficient.

The same process can be applied when looking at statement (2) on its own. We must try values of x that fall in the two critical regions which meet the criteria in the statement. Thus, we must test values in the region -7 < x < 2 and values in the region x > 2. When we do, we find that y is not always equal to 9.

When we look at the two statements together, the only critical region to be considered is -7 < x < 2. Now the two statements are sufficient (y is always 9 in this region) and the correct answer is C, statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.

-A

Acecoolan,
No probs! As Logitech very rightly said we are all here to help each other.

Thanks for the official soln!


Logitech,

ST1+ST2

Y can be 9 between -7<x<2

Did u mean y is always 9 beacuse may be 9 would be E) and not C)?

Did u mean y is always 9 beacuse may be 9 would be E) and not C)?

EGJACTlY:)

logitech@....

it can be E as well right ?? i had the same thign running in my head !!

vishu

it can be E as well right ?? i had the same thign running in my head !!

Probably he meant to write always 9. As I pointed -7<x<2 the y value is always 9

One defenite answer so C)