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

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Director
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Re: How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?  [#permalink]

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04 Jul 2019, 18:33
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jfranciscocuencag

I am not talking about the sign of the value I am introducing, I am talking about the absolute value itself.

for example, if we examine |x-3|, it will be always positive because of the absolute sign,
but what is the true value inside???
is it really (x-3) or is it (3-x) --> (both under absolute value will give the same end result, but is |x-3| positive because of itself, or is it negative but the absolute sign converted it?

so when we try a value from the range:
if (x-3) gave us positive (or zero) value, so it was actually (x-3)
if (x-3) gave us negative value, so it is actually (3-x)

I hope it helps
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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.
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Posts: 75
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.
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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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How many different values of y satisfy |y + 3| = |8 + y| + |4 - y| ?   [#permalink] 24 Jul 2019, 06:42

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