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# If Y = |X + 1| - |X-2|, then

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Senior Manager
Joined: 24 Apr 2016
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If Y = |X + 1| - |X-2|, then [#permalink]

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06 Feb 2017, 13:42
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If $$Y = |X + 1| - |X-2|$$, then

(a) $$-3 \leq Y \leq 0$$
(b) $$-3 \leq Y \leq 3$$
(c) $$Y \leq -3$$
(d) $$Y \geq -3$$
(e) No Solution
[Reveal] Spoiler: OA

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Director
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Re: If Y = |X + 1| - |X-2|, then [#permalink]

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06 Feb 2017, 18:22
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quantumliner wrote:
If Y = |X + 1| - |X-2|, then

(a) -3 <= Y <=0
(b) -3 <= Y <=3
(c) Y <=-3
(d) Y >=-3
(e) No Solution

3 ranges to define

1) x< -1 then y= -3
2) -1<=x<2 then y = 2x-1
3) x>= 2 then y=3

as second condition dependent on value of x
thus from range 1 & 2
-3 <= Y <=3

Ans B

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Intern
Joined: 16 Jan 2017
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Re: If Y = |X + 1| - |X-2|, then [#permalink]

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09 Feb 2017, 05:30
rohit8865 wrote:

3 ranges to define

1) x< -1 then y= -3
2) -1<=x<2 then y = 2x-1
3) x>= 2 then y=3

as second condition dependent on value of x
thus from range 1 & 2
-3 <= Y <=3

Ans B

How did you came up with the 3 ranges and how to define them? I dont understand what you are doing.
Thanks

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Director
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Re: If Y = |X + 1| - |X-2|, then [#permalink]

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09 Feb 2017, 06:08
2
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maxschmid wrote:
rohit8865 wrote:

3 ranges to define

1) x< -1 then y= -3
2) -1<=x<2 then y = 2x-1
3) x>= 2 then y=3

as second condition dependent on value of x
thus from range 1 & 2
-3 <= Y <=3

Ans B

How did you came up with the 3 ranges and how to define them? I dont understand what you are doing.
Thanks

maxschmid

for such questions always do the below suggested

Ix+1I will be 0 when x= -1
similarly Ix-2I will be 0 when x=2

thus we have boundaries defined as -1 and 2
so i have checked on both sides of boundaries defined in three steps for value y

1) x< -1 then y= -3
2) -1<=x<2 then y = 2x-1
3) x>= 2 then y=3

hope now u can understand

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Re: If Y = |X + 1| - |X-2|, then [#permalink]

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13 Feb 2017, 16:05
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Expert's post
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quantumliner wrote:
If Y = |X + 1| - |X-2|, then

(a) -3 <= Y <=0
(b) -3 <= Y <=3
(c) Y <=-3
(d) Y >=-3
(e) No Solution

Since the expressions in the absolute value will equal zero when X = -1 and X = 2, we need to investigate the following three cases:

i) X < -1, ii) -1 < X < 2, and iii) X > 2

Now let’s analyze each case.

i) If X < -1, we see that both of the expressions inside the absolute values are negative, and thus:

Y = -(X - 1) - [-(X - 2)]

Y = - X -1 + X - 2

Y = -3

ii) If -1 < X < 2, then the first expression is positive but the second expression is negative; thus:

Y = X + 1 - [-(X - 2)]

Y = X + 1 + X - 2

Y = 2X -1

Now, recall that -1 < X < 2, so

-2 < 2X < 4

-3 < 2X - 1 < 3

Since Y = 2X - 1, -3 < Y < 3.

iii) If X > 2, then both expressions inside the absolute value are positive; thus:

Y = X + 1 - (X - 2)

Y = X + 1 - X + 2

Y = 3

Combining the results of the three cases, we see that -3 ≤ Y ≤ 3.

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Re: If Y = |X + 1| - |X-2|, then [#permalink]

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15 Feb 2017, 03:45
JeffTargetTestPrep wrote:
quantumliner wrote:
If Y = |X + 1| - |X-2|, then

(a) -3 <= Y <=0
(b) -3 <= Y <=3
(c) Y <=-3
(d) Y >=-3
(e) No Solution

Since the expressions in the absolute value will equal zero when X = -1 and X = 2, we need to investigate the following three cases:

i) X < -1, ii) -1 < X < 2, and iii) X > 2

Now let’s analyze each case.

i) If X < -1, we see that both of the expressions inside the absolute values are negative, and thus:

Y = -(X - 1) - [-(X - 2)]

Y = - X -1 + X - 2

Y = -3

ii) If -1 < X < 2, then the first expression is positive but the second expression is negative; thus:

Y = X + 1 - [-(X - 2)]

Y = X + 1 + X - 2

Y = 2X -1

Now, recall that -1 < X < 2, so

-2 < 2X < 4

-3 < 2X - 1 < 3

Since Y = 2X - 1, -3 < Y < 3.

iii) If X > 2, then both expressions inside the absolute value are positive; thus:

Y = X + 1 - (X - 2)

Y = X + 1 - X + 2

Y = 3

Combining the results of the three cases, we see that -3 ≤ Y ≤ 3.

I have a query regarding the range. Shouldn't it be -1 <= X < 2 and X >= 2

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Re: If Y = |X + 1| - |X-2|, then [#permalink]

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15 Feb 2017, 05:04
2
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warriorguy wrote:

I have a query regarding the range. Shouldn't it be -1 <= X < 2 and X >= 2

Dear warriorguy, Graphical illustration will clear your doubt.

When $$x = 2$$

$$Y = |x+1| - |x-2| = |2+1| - |2-2| = |3| + |0| = 3$$

Coordinate 1 $$(2, 3)$$

When $$x = -1$$

$$Y = |x+1| - |x-2| = |-1+1| - |-1-2| = |0| - |3| = -3$$

Coordinate 2 $$(-1, -3)$$

Therefore, the solution is $$-3 ≤ y ≤ 3$$
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Re: If Y = |X + 1| - |X-2|, then [#permalink]

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16 Feb 2017, 13:13
1
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Expert's post
Hi All,

This question can be solved by TESTing VALUES.

We're told that Y = |X + 1| - |X-2|. We're asked to find the range of value for Y.

IF....
X = 0, then Y = |1| - |-2| = -1, so Y can equal -1. Eliminate Answers C and E. Considering the three remaining answers, we know that Y either has an "upper limit" or it does not, so let's see what happens if we make X really big or really small....

IF...
X = 100, then Y = |101| - |98| = 3. This is interesting, since we've appeared to now randomly hit the 'upper limit' in Answer B. Eliminate Answer A. What if we try something even bigger....
X = 1000, then Y = |1001| - |998| = 3. This is the exact SAME value... It certainly looks like we've found the upper limit, but just to be sure, I'll do one more Test...

IF....
X = -50, then Y = |-49| - |-52| = -3. We clearly have the range now.

[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
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# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Last edited by EMPOWERgmatRichC on 24 Sep 2017, 12:27, edited 1 time in total. Kudos [?]: 3688 [1], given: 173 Manager Joined: 30 May 2012 Posts: 217 Kudos [?]: 84 [1], given: 151 Location: United States (TX) Concentration: Finance, Marketing GPA: 3.3 WE: Information Technology (Consulting) Re: If Y = |X + 1| - |X-2|, then [#permalink] ### Show Tags 23 Sep 2017, 12:15 1 This post received KUDOS EMPOWERgmatRichC wrote: ... IF.... X = 0, then Y = |1| - |-2| = 1, so Y can equal 1. ... Rich How so? How does one approach this via a number line? Kudos [?]: 84 [1], given: 151 Manager Joined: 30 May 2012 Posts: 217 Kudos [?]: 84 [0], given: 151 Location: United States (TX) Concentration: Finance, Marketing GPA: 3.3 WE: Information Technology (Consulting) Re: If Y = |X + 1| - |X-2|, then [#permalink] ### Show Tags 23 Sep 2017, 12:23 mikemcgarry - Could you help me with plotting a solution on the number line, please? Kudos [?]: 84 [0], given: 151 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 10391 Kudos [?]: 3688 [0], given: 173 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If Y = |X + 1| - |X-2|, then [#permalink] ### Show Tags 24 Sep 2017, 12:29 Hi Blackbox, Thanks for catching the error; I've updated my explanation. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If Y = |X + 1| - |X-2|, then   [#permalink] 24 Sep 2017, 12:29
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