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

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Senior Manager
Joined: 12 Sep 2017
Posts: 306
How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

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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?
Senior Manager
Joined: 05 Mar 2017
Posts: 261
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Hospitality and Tourism)
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

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07 Jul 2019, 00:26
Zeros of the equation:
y+3=0
8+y=0
4-y=0

y=-8; -3; 4

1st case: y<=-8

-y-3=-8-y+4-y >>
y=-1 (doesn't meet the criteria y<=-8)

2nd case: -8<=y<=-3
-y-3=8+y+4-y
-y-3=12
-y=15
y=-15 (doesn't meet the criteria -8<=y<=-3)

3rd case: -3<=y<=4
y+3=8+y+4-y
y+3=12
y=9(doesn't meet the criteria -8<=y<=-3)

4th case: y>=4
y+3=8+y-4+y
y=-1 (doesn't meet the criteria y>=4)

No solution and Hence The answer is A.
BSchool Moderator
Joined: 29 Apr 2019
Posts: 78
Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

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17 Jul 2019, 05:46

I falter a lot on problems with multiple mods in a equation vis-a-vis mods on either side of the equation.

It'll be really helpful if one of you could explain how to reduce these to a simplest (non mod) form.
Director
Joined: 27 May 2012
Posts: 936
How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

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24 Jul 2019, 06:42
Bunuel wrote:
How many different values of $$y$$ satisfy $$|y + 3| = |8 + y| + |4 - y|$$ ?

A. 0
B. 1
C. 2
D. 3
E. 4

 This question was provided by Crack Verbal for the Game of Timers Competition

Just a note:

Actually this a repeat of a very old question already discussed here in GMAT ClUB, does not seem an original question .Below is the link,In the question in the link , just change the variable x to y and bring |4-y| to LHS.

https://gmatclub.com/forum/x-3-4-x-8-x- ... l#p1193846
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- Stne
How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?   [#permalink] 24 Jul 2019, 06:42

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