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

It is currently 14 Oct 2019, 06:31

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

How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 25 Aug 2015
Posts: 45
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 10:05
As y can be negative of positive for absolute value to hold, then any 2 values for y.

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 30 May 2018
Posts: 156
Location: Canada
GMAT 1: 710 Q49 V36
GPA: 3.8
Premium Member Reviews Badge CAT Tests
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 10:33
1
Answer is 0.

Take four possible cases of y, i.e, y<-8, -8<y<-3, -3<y<4 and y>4. In each case, solve the equation, y gets a value outside of assumed range of each case.
Senior Manager
Senior Manager
User avatar
P
Joined: 31 May 2018
Posts: 413
Location: United States
Concentration: Finance, Marketing
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 10:37
1
here the solution of the question
Attachments

got.png
got.png [ 33.65 KiB | Viewed 517 times ]

Intern
Intern
avatar
B
Joined: 05 Jun 2018
Posts: 31
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 10:52
1
Four scenarios

4>y>0

y+3=y+8+4-y
y=9

Not possible

y>4

y+3=8+y+y-4
y=-1

Not possible

y<-8
-y-3=-y-8+4-y
y=-1
Not possible

-3>y>-8
-y-3=8+y+4-y
y=-15
Not possible

0>y>-3
y+3=8+y+4-y
y=9

Not possible

Thus, 0 values
Manager
Manager
avatar
S
Joined: 12 Mar 2018
Posts: 83
Location: United States
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 11:12
1
It took me way too long to solve this problem (3m and 46s)

I followed the 3 step approach explained in the Absolute Value theory here (https://gmatclub.com/forum/math-absolut ... 86462.html), and got the answer 0, which is option A.

But obviously from the time standpoint, close to 4 mins is terrible for this kind of question.
Can one of the experts help me with a quicker/alternate solution that can be done in less than 2 mins?

Here are the details of what I did:

Step 1: Identified the critical points, -8, -3 and 4 and set conditions, y < -8, -8 <= y < -3, -3 <= y < 4, and y >= 4
Step 2: For each one of the regions listed in step 1, used conditions to open modulus and solve for y
Step 3: Checked if the resulting y value falls within the region for each one of the ranges in Step 1. None of the y values did, so the answer is 0
Manager
Manager
avatar
S
Joined: 06 Aug 2018
Posts: 98
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 11:26
Basically there can be different combinations made

Firstly all r positive

1
|y+3|=|8+y|+|4−y|

y+3=8+y+4-y
y=9

Putting 9 in equation
Both sides are not equal

2. If one is negative

y+3=-8-y+4-y
y=-7/3

This satisfies the eqaution

3 both negative

y+3=-y-8-4+y
y=-15

Again this doesn't satify

Now -y-3=y-8+4-y
y=1 again this doesn't satisfy equation ,

Then -y-3=-y-8+4-y
y=-1

Then -y-3=-y-8-4+y
y=9

This again doesn't satisfy

There is only one solution as -7/3

Posted from my mobile device
Manager
Manager
avatar
G
Joined: 04 Apr 2015
Posts: 218
Reviews Badge
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 11:51
1
firstly analyzing the problem i was confused whether to plug in or form equation with cases '

however
considering the equation
|y+3|=|8+y|+|4−y|
let A= |y+3|
B= |8+y|
C=|4−y|

A is always positive : or zero
B is always positive or zero
C is always positive or zero

lets compare A and B
|y+3|=|8+y|they can never be equal distance of one number and 3 on number line cannot be equal to distance of same number and 8 so no value exists

adding C to the equation further complicates the issue as C is positive and distance of B and C together cannot be equal to A

so answer A : no value exist
Senior Manager
Senior Manager
avatar
G
Joined: 18 May 2019
Posts: 343
GMAT ToolKit User Premium Member CAT Tests
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 12:09
1
|y+3|=|8+y|+|4-y|
The center points can be gotten by equating the absolute values to zero. Hence the key points are -3, -8 and 4.
The possible conditions are
y<-8; -8<=y<-3; -3<=y<4; and y>=4.
When y<-8,
-(y+3)=-(8+y)+(4-y)
Solving for y yields y=-1
Since -1 does not fit into the range of values y<-8, we reject this solution.
When -8<=y<-3,
-(y+3)=(8+y)+(4-y)
y=-15. -15 does not fall within the above range hence we reject this solution as well.
-3<=y<4;
(y+3)=(8+y)+(4-y)
Solving for y, y=9. And nine falls outside the range, hence we reject this solution as well.
y>=4
(y+3)=(8+y)-(4-y)
y=1, which is not greater than 4, hence we reject this solution as well.
This means there is no solution to this equation. Hence choice A is the right answer.

Posted from my mobile device
Manager
Manager
avatar
G
Joined: 06 Feb 2019
Posts: 108
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 12:30
1
there is no such y that will match the equation:
positive numbers are out because |y+3| will be always less that |8+y| (keeping in mind that |4-y| may not be negative.
zero is out
negative numbers will make |4-y| big positive number

answer - A (0)
Manager
Manager
User avatar
G
Joined: 12 Jan 2018
Posts: 116
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 12:56
1
This equation has 3 critical points, -3,-8, 4. Hence, 4 conditions to check.

1. y>4
(y+3)=(8+y)-(4-y) Since, |x|=x if x>/=0. |x|=-x if x<0
y=-1 , but condition is y>4. No solution in this range

2. -3<y</=4
(y+3)=(8+y)+(4-y)
y=11, outside the range. No solution

3.- -8<y</=-3
-(y+3)=(8+y)+(4-y)
y=-15
_________________
"Remember that guy that gave up?
Neither does anybody else"
Manager
Manager
avatar
G
Joined: 30 Nov 2017
Posts: 193
WE: Consulting (Consulting)
Premium Member
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 15:39
Explanation
Given; |y+3| = |8+y| + |4-y|
Solving for y;
Condition 1
y+3 = 8+y+4-y
This gives; y = 9
Testing y = 9 in the equation above
We have; |9+3| = |8+9| + |4-9|
Thus, 12 = 17 - 5
Therefore, 12 = 12 (y=9 satisfies the equation)
Condition 2
If we negate the left side of the equation, we have
-y-3 = 8+y+4-y
This gives; y=-15
Testing y=-15 in the original equation
We have; -15+3 = 8-15+4+15
-12 = 12 (y = -15 does not satisfy the equation)
Condition 3
Negating only one side of the equation on the right side, we have
y+3 = 8+y - (4-y)
y+3 = 8+y-4+y
y+3 = 4+2y
Thus, y=-1
Testing y=-1 in the original equation
We have; -1+3 = 8-1 + 4+1
2 = 12 (y=-1 does not satisfy the equation)
Therefore, the equation has only one solution and it's answer choice B.

Posted from my mobile device
_________________
Be Braver, you cannot cross a chasm in two small jumps...
Manager
Manager
User avatar
G
Joined: 28 Jan 2019
Posts: 125
Location: Peru
Premium Member
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 17:53
1
There are 4 ranges:
Y≤ -8, Y =-1
-8≤Y≤-3, Y= -15
-3≤Y≤4, Y = 15
Y≥4, Y = -1

So, none of them comply with the ranges, so (A)

None of them satisfy the equation, so (A)
Intern
Intern
avatar
B
Joined: 12 Jul 2014
Posts: 3
Premium Member CAT Tests
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 18:08
C - 2 values possible
Intern
Intern
avatar
B
Joined: 22 Jun 2019
Posts: 41
Location: Canada
Concentration: Operations, Organizational Behavior
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 20:00
1
tried plugging in several numbers and realized it never matches so A)
Manager
Manager
User avatar
G
Joined: 08 Jan 2018
Posts: 129
CAT Tests
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 21:49
1
The three critical values are -8, -3 and 4

We can have 4 conditions:

1. y < -8:
-(y + 3) = - (8 + y) + (4 – y)
=> y = -1
This does not fall in the range of y < -3. Therefore, we can reject the solution.

2. -8 <= y < -3:
-(y + 3) = (8 + y) + (4 – y)
=> y = -15
This does not fall in the range of -8 <= y < -3. Therefore, we can reject the solution.

3. -3 <= y <4
(y + 3) = (8 + y) + (4 – y)
=> y = 9
This does not fall in the range of -3 <= y <4. Therefore, we can reject the solution.

4. y >= 4
(y + 3) = (8 + y) – (4 – y)
=> y = -1
This does not fall in the range of y >= 4. Therefore, we can reject the solution.

Therefore, no value of y satisfy. Answer A.
Senior Manager
Senior Manager
avatar
P
Joined: 30 Sep 2017
Posts: 375
Concentration: Technology, Entrepreneurship
GMAT 1: 720 Q49 V40
GPA: 3.8
WE: Engineering (Real Estate)
Premium Member Reviews Badge CAT Tests
How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post Updated on: 03 Jul 2019, 22:22
1
QUESTION: How many different values of y satisfy |y+3|=|8+y|+|4−y| ?

Each |y+3|, |8+y|, and |4−y| has a value of 0 or positive number.

For y>= -3, |y+3| is always less than |8+y|
--> (y+3) < (y+8)
--> 3 < 8
Hence, |y+3| is also always less than |8+y| + |4−y|

For y< -3, |y+3| is always less than |4-y|
--> -(y+3) < (4-y)
--> -3 < 4
Hence, |y+3| is also always less than |8+y| + |4−y|

As discussed, for any y value, |y+3| will never be equal to |8+y|+|4−y|

Answer is (A)

Originally posted by chondro48 on 03 Jul 2019, 22:05.
Last edited by chondro48 on 03 Jul 2019, 22:22, edited 1 time in total.
Manager
Manager
avatar
S
Joined: 24 Jan 2019
Posts: 107
Location: India
Concentration: Strategy, Finance
GMAT 1: 730 Q51 V38
GPA: 4
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 03 Jul 2019, 22:20
1
This is a tricky question. First of we should understand that (Y+3), (8+Y) & (4-Y) will change signs at -3, -8 & +4 respectively. These 3 points are the minimum (| f(y)|=0) for given 3 modulus terms independently.

These 3 points will create 4 intervals on a number line as per following:

(1) Y< -8
(2) -8 <= Y < -3
(3) -3 <= Y < 4
(4) Y >= 4

Open all 3 modulus in each interval and solve for Y. Value which we get for Y in each interval doesn't belong to corresponding interval.

So, effectively we will have "0" values of Y which can satisfy given equation.

ANSWER : A
Senior Manager
Senior Manager
User avatar
S
Joined: 12 Sep 2017
Posts: 301
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 04 Jul 2019, 17:37
Mahmoudfawzy83 wrote:
to find the possible values of y in \(|y+3|=|8+y|+|4−y|\), there are 4 intervals to examine:
\(x≥4\) --> y+3 = 8+y + y-4 --> \(y= -1\) --> invalid because not within stated range
\(4>x ≥-3\) --> y+3 = 8+y + 4-y --> \(y= 9\) --> invalid because not within stated range
\(-3>x ≥-8\) --> -y-3 = 8+y + 4-y --> \(y= -15\) --> invalid because not within stated range
\(-8 ≥x\) --> -y-3 = -8-y + 4-y --> \(y= -1\) --> invalid because not within stated range

so there is acceptable value upon validating, so A


Hello Mahmoudfawzy83!

How do we know which term we have to change to neg depending the range?

Kind regards!
Director
Director
User avatar
V
Status: Manager
Joined: 27 Oct 2018
Posts: 670
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)
GMAT ToolKit User
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 04 Jul 2019, 17:51
1
hi jfranciscocuencag
jfranciscocuencag wrote:
How do we know which term we have to change to neg depending the range?


By trying any value from the range, and see whether it will stay positive or negative.
lets take \(x>4\)
choose any number ... 5 or 100 .. the same will do:
when substituting y with 5, y+3 will be 8, so keep it--> +y+3
when substituting y with 5, 8+y will be 13, so keep it --> +8+y
when substituting y with 5, 4-y will be -1, so invert the signs --> -4+y

lets take \(-8 >x\)
choose any number ... -9 or -100 .. the same will do:
when substituting y with -9, y+3 will be -6, so invert the signs--> -y-3
when substituting y with -9, 8+y will be -1, so invert the signs --> -8-y
when substituting y with -9, 4-y will be 13, so keep it --> +4-y

It is tedious, but by practice, you will used to it. It is a very important step to use with every absolute value question.
_________________
Thanks for Kudos
Senior Manager
Senior Manager
User avatar
S
Joined: 12 Sep 2017
Posts: 301
How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

Show Tags

New post 04 Jul 2019, 18:19
choose any number ... 5 or 100 .. the same will do:
when substituting y with 5, y+3 will be 8, so keep it--> +y+3
when substituting y with 5, 8+y will be 13, so keep it --> +8+y
when substituting y with 5, 4-y will be -1, so invert the signs --> -4+y

lets take \(-8 >x\)
choose any number ... -9 or -100 .. the same will do:
when substituting y with -9, y+3 will be -6, so invert the signs--> -y-3
when substituting y with -9, 8+y will be -1, so invert the signs --> -8-y
when substituting y with -9, 4-y will be 13, so keep it --> +4-y

Mahmoudfawzy83

I have some doubt regarding the second example:

when substituting y with -9, y+3 will be -6, so invert the signs--> -y-3
when substituting y with -9, 8+y will be -1, so invert the signs --> -8-y

The numbers are -6 and -1 so they didn't change the sign, they are still neg. Why do we have to invert the sign here?
GMAT Club Bot
How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?   [#permalink] 04 Jul 2019, 18:19

Go to page   Previous    1   2   3   4    Next  [ 64 posts ] 

Display posts from previous: Sort by

How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?

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





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