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What is the value of |x+5| + |x-3| ?

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What is the value of |x+5| + |x-3| ? [#permalink]

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What is the value of |x+5| + |x-3| ?

1) \(x^2\) < 25

2) \(x^2\) > 9
[Reveal] Spoiler: OA

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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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New post 03 Apr 2016, 08:45
lpetroski wrote:
What is the value of |x+5| + |x-3| ?

1) \(x^2\) < 25

2) \(x^2\) > 9



So, at first glance I thought it was E, but when combining the inequalities I got -2 < x < 2, which all of the values -1, 0 and 1 cause the equation to equal 8 -- but the OA is E - so what did I do wrong here? Thanks!!

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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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lpetroski wrote:
lpetroski wrote:
What is the value of |x+5| + |x-3| ?

1) \(x^2\) < 25

2) \(x^2\) > 9



So, at first glance I thought it was E, but when combining the inequalitiesI got -2 < x < 2, which all of the values -1, 0 and 1 cause the equation to equal 8 -- but the OA is E - so what did I do wrong here? Thanks!!



Hi
the highlighted portion is wrong..

1) \(x^2\) < 25

this gives -5<x<5
|x+5| + |x-3|
if 4 then |4+5|+|4-3|=10
if -4 then |-4+5|+|-4-3|=8
Insuff

2) \(x^2\) > 9
this gives x<-3 or x>3
same this is also not suff

combined
either -5<x<-3 OR 3<x<5..
substitute 4 ans is 10
substitute -4 ans is 8..
Insuff
E
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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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lpetroski wrote:
lpetroski wrote:
What is the value of |x+5| + |x-3| ?

1) \(x^2\) < 25

2) \(x^2\) > 9



So, at first glance I thought it was E, but when combining the inequalities I got -2 < x < 2, which all of the values -1, 0 and 1 cause the equation to equal 8 -- but the OA is E - so what did I do wrong here? Thanks!!


First of all the solution is -5<x<-3 or 3<x<5. Next, you assume with no ground that x is an integer.

Hope it helps.
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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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New post 04 Apr 2016, 05:55
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of |x+5| + |x-3| ?

1) x^2 < 25

2) x^2 > 9


When you modify the original condition and the question, a case where sum of 2 absolute values is derived is that the range of in between gets a consistent answer, which is -5<=x<=3?.
There is 1 variable(x), which should match with the number of equations. so you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
When it comes to inequality questions, if range of que includes range of con, use the fact that that con is sufficient.
For 1), in -5<x<5, the range of que doesn't include the range of con, which is not sufficient.
For 2), in x<-3 or 3<x, the range of que doesn't include the range of con, which is not sufficient.
When 1) & 2), in -5<x<-3 or 3<x<5, the range of que doesn't include the range of con, which is not sufficient.
Thus, the answer is E.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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What is the value of |x+5| + |x-3| ? [#permalink]

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New post 18 Jul 2016, 08:52
What is the value of |x+5| + |x-3| ?

(1) x^2 < 25
(2) x^2 > 9

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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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New post 18 Jul 2016, 09:04
nishatfarhat87 wrote:
What is the value of |x+5| + |x-3| ?

(1) x^2 < 25
(2) x^2 > 9


Topic Merged. Please refer to the above discussion.

Rules for posting: rules-for-posting-please-read-this-before-posting-133935.html#p1092822

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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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New post 31 Jul 2016, 00:27
Vyshak wrote:
nishatfarhat87 wrote:
What is the value of |x+5| + |x-3| ?

(1) x^2 < 25
(2) x^2 > 9


Topic Merged. Please refer to the above discussion.

Rules for posting: rules-for-posting-please-read-this-before-posting-133935.html#p1092822


I correctly determined the range of x as per (1). But it turns out that only X= 4 & X = -4 give different answers, making statement 1 insufficient.
All other numbers in -5<x<5 give the solution = 8.

I tested 2-3 numbers except (4,-4) and marked the statement 1 sufficient.

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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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New post 31 Jul 2016, 00:40
ajay2121988 wrote:
Vyshak wrote:
nishatfarhat87 wrote:
What is the value of |x+5| + |x-3| ?

(1) x^2 < 25
(2) x^2 > 9


Topic Merged. Please refer to the above discussion.

Rules for posting: rules-for-posting-please-read-this-before-posting-133935.html#p1092822


I correctly determined the range of x as per (1). But it turns out that only X= 4 & X = -4 give different answers, making statement 1 insufficient.
All other numbers in -5<x<5 give the solution = 8.

I tested 2-3 numbers except (4,-4) and marked the statement 1 sufficient.


why did ignore (4,-4)? It is given that -5<x<5 as per statement 1. That means x could be -4 or 4. Hence, Statement 1 is insufficient.
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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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New post 31 Jul 2016, 00:42
chetan2u wrote:
lpetroski wrote:
lpetroski wrote:
What is the value of |x+5| + |x-3| ?

1) \(x^2\) < 25

2) \(x^2\) > 9



So, at first glance I thought it was E, but when combining the inequalitiesI got -2 < x < 2, which all of the values -1, 0 and 1 cause the equation to equal 8 -- but the OA is E - so what did I do wrong here? Thanks!!



Hi
the highlighted portion is wrong..

1) \(x^2\) < 25

this gives -5<x<5
|x+5| + |x-3|
if 4 then |4+5|+|4-3|=10
if -4 then |-4+5|+|-4-3|=8
Insuff

2) \(x^2\) > 9
this gives x<-3 or x>3
same this is also not suff

combined
either -5<x<-3 OR 3<x<5..
substitute 4 ans is 10
substitute -4 ans is 8..
Insuff
E


For condition 1, you directly checked for x = 4,-4. Why ? That must have saved a lot of time. I started checking with 1,2,3,-1,-2,-3 (all give result=8,spent 15-20 seconds doing so) & didn't check for 4,-4, hence marked the condition sufficient.
Given the time constraints, how can one check all conditions in a DS question? Or am I missing some point ?

Thanks,

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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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New post 31 Jul 2016, 00:45
Rules for posting: rules-for-posting-please-read-this-before-posting-133935.html#p1092822[/b][/quote]

I correctly determined the range of x as per (1). But it turns out that only X= 4 & X = -4 give different answers, making statement 1 insufficient.
All other numbers in -5<x<5 give the solution = 8.

I tested 2-3 numbers except (4,-4) and marked the statement 1 sufficient.[/quote]

why did ignore (4,-4)? It is given that -5<x<5 as per statement 1. That means x could be -4 or 4. Hence, Statement 1 is insufficient.[/quote]

I didn't check all because I thought time is running & generally testing 2-3 conditions reveals the issue. That's why.

Ok, lesson learnt. Will check all conditions.
Thanks !

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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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New post 11 Sep 2016, 14:16
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we have three concerned ranges

x < -3 here equation will be -2x-2
-3 =< x < 5 here equation value is 8
x >= 5 Here equation value will be 2x + 2

so only for 2nd range we have a fixed value.

Stmt 1 implies -5 < x < 5 insufficient as it covers more than one of the three above mentioned ranges.
Stmt 2 implies x < -3 and x > 3 insufficient as it covers more than one of the three above mentioned ranges.

Combining statement 1 & 2 -5<x < -3 and 3<x<5 insufficient as it covers more than one of the three above mentioned ranges.

Ans E
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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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New post 31 Jul 2017, 10:48
Bunuel, when we simplify x^2<25, do we write |x|<5 or x<|5| ?

Thanks

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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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Re: What is the value of |x+5| + |x-3| ? [#permalink]

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New post 01 Aug 2017, 02:50
Bunuel wrote:
lpetroski wrote:
lpetroski wrote:
What is the value of |x+5| + |x-3| ?

1) \(x^2\) < 25

2) \(x^2\) > 9



So, at first glance I thought it was E, but when combining the inequalities I got -2 < x < 2, which all of the values -1, 0 and 1 cause the equation to equal 8 -- but the OA is E - so what did I do wrong here? Thanks!!


First of all the solution is -5<x<-3 or 3<x<5. Next, you assume with no ground that x is an integer.

Hope it helps.

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Re: What is the value of |x+5| + |x-3| ?   [#permalink] 01 Aug 2017, 02:50
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