GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Nov 2019, 02:40

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
avatar
G
Joined: 24 Apr 2016
Posts: 317
If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post 06 Feb 2017, 14:42
3
25
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (02:05) correct 35% (02:02) wrong based on 412 sessions

HideShow timer Statistics

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
Most Helpful Expert Reply
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2812
Re: If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post 13 Feb 2017, 17:05
3
6
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.

Answer: B
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

General Discussion
Director
Director
User avatar
D
Joined: 05 Mar 2015
Posts: 985
Reviews Badge
Re: If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post 09 Feb 2017, 07:08
3
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
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15503
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post Updated on: 24 Sep 2017, 13:27
3
1
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.

Let's start with something easy....

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.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★

Originally posted by EMPOWERgmatRichC on 16 Feb 2017, 14:13.
Last edited by EMPOWERgmatRichC on 24 Sep 2017, 13:27, edited 1 time in total.
Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1347
Location: Malaysia
GMAT ToolKit User
Re: If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post 15 Feb 2017, 06:04
2
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 \(-3 ≤ y ≤ 3\)
Attachments

Untitled.jpg
Untitled.jpg [ 93.72 KiB | Viewed 4041 times ]


_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/
Director
Director
User avatar
D
Joined: 05 Mar 2015
Posts: 985
Reviews Badge
Re: If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post 06 Feb 2017, 19:22
1
2
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
Intern
Intern
avatar
B
Joined: 16 Jan 2017
Posts: 5
Re: If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post 09 Feb 2017, 06:30
1
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
Manager
Manager
User avatar
S
Joined: 30 May 2012
Posts: 197
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

New post 23 Sep 2017, 13:15
1
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?
Retired Moderator
avatar
P
Joined: 04 Aug 2016
Posts: 475
Location: India
Concentration: Leadership, Strategy
GPA: 4
WE: Engineering (Telecommunications)
Re: If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post 15 Feb 2017, 04:45
1
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.

Answer: B



I have a query regarding the range. Shouldn't it be -1 <= X < 2 and X >= 2
Manager
Manager
User avatar
S
Joined: 30 May 2012
Posts: 197
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

New post 23 Sep 2017, 13:23
mikemcgarry - Could you help me with plotting a solution on the number line, please?
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15503
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post 24 Sep 2017, 13:29
Hi Blackbox,

Thanks for catching the error; I've updated my explanation.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Manager
User avatar
G
Joined: 11 Feb 2013
Posts: 216
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
GMAT ToolKit User Premium Member Reviews Badge
If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post Updated on: 01 Nov 2019, 20:11
The maximum/Minimum DIFFERENCE between two ABSOLUTE values is THE ABSOLUTE VALUE of their individual DIFFERENCE .
For example, if two values are a&b.
we know, their individual absolute values are /a/ and /b/ and
DIFFERENCE between a & b= a-b.
The maximum/Minimum DIFFERENCE between two ABSOLUTE values= /(a-b)/

Originally posted by BelalHossain046 on 01 Nov 2019, 20:03.
Last edited by BelalHossain046 on 01 Nov 2019, 20:11, edited 1 time in total.
Manager
Manager
User avatar
G
Joined: 11 Feb 2013
Posts: 216
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
GMAT ToolKit User Premium Member Reviews Badge
Re: If Y = |X + 1| - |X-2|, then  [#permalink]

Show Tags

New post 01 Nov 2019, 20:10
Back to the question:
Max and min value of y=
y =|X+1|−|X−2|
[The maximum/Minimum DIFFERENCE between two ABSOLUTE values is THE ABSOLUTE VALUE of their individual DIFFERENCE].
=|(x+1)-(x-2)|
=|3|
=+3 or -3
So maximum value of y =3 and minimum value of y= -3.
In other words, Y must be in the range of -3 and +3.
GMAT Club Bot
Re: If Y = |X + 1| - |X-2|, then   [#permalink] 01 Nov 2019, 20:10
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne