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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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03 Apr 2016, 08:43
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72% (00:59) correct 28% (00:57) wrong based on 697 sessions

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

1) $$x^2$$ < 25

2) $$x^2$$ > 9
Math Expert
Joined: 02 Aug 2009
Posts: 6800
Re: What is the value of |x+5| + |x-3| ?  [#permalink]

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03 Apr 2016, 09:05
10
8
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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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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Posts: 49303
Re: What is the value of |x+5| + |x-3| ?  [#permalink]

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03 Apr 2016, 09:09
6
1
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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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.

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

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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.

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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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.

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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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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31 Jul 2016, 00:45

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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11 Sep 2016, 14:16
1
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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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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01 Aug 2017, 00:25
1
1
OreoShake wrote:
Bunuel, when we simplify x^2<25, do we write |x|<5 or x<|5| ?

Thanks

$$x^2 < 25$$

Take the square root from both sides: $$|x| < 5$$ (recall that $$\sqrt{x^2}=|x|$$).

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

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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.

An eye opener...

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

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03 Dec 2017, 18:48
Since each statement alone is insuficient, answer could be C or E.
When you put them together, you have 9<x²<25. At any moment the stem tells us x is an integer, so x could be any number between 3 and 5 (or between -3 and -5), for example 4,3 (4,3²=18,49, which is in the interval). So, we know it is impossible to determine the value of the |x+5| + |x-3|. Answer is E.
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Re: What is the value of |x+5| + |x-3| ?  [#permalink]

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08 Jul 2018, 10:31
Bunuel wrote:
OreoShake wrote:
Bunuel, when we simplify x^2<25, do we write |x|<5 or x<|5| ?

Thanks

$$x^2 < 25$$

Take the square root from both sides: $$|x| < 5$$ (recall that $$\sqrt{x^2}=|x|$$).

Hope it's clear.

Bunuel

What are the critical points or ranges?
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What is the value of |x+5| + |x-3| ?  [#permalink]

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11 Jul 2018, 07:52
lpetroski wrote:
What is the value of |x+5| + |x-3| ?

1) $$x^2$$ < 25

2) $$x^2$$ > 9

Solved with thinking as x must be <+5 or - 5 OR > +3 or -3

someone will think that x must be 4 ! but it seems a trap. there is no info about x such that x has to be an integer only.

therefore x can take multiple value even if both st are combined.

ans = E
What is the value of |x+5| + |x-3| ? &nbs [#permalink] 11 Jul 2018, 07:52
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