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Which of the following sets includes ALL of the solutions of

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Re: Which of the following sets includes ALL of the solutions of  [#permalink]

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New post 02 Jul 2013, 20:14
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jjack0310 wrote:
VeritasPrepKarishma wrote:

Ok, so how did you plug in? I an ignoring options (A) and (B) and focusing on just (C)

Option (C) {-4, 0, 1, 4, 5, 6}

|x-2|-|x-3|=|x-5|
You put x = -4. It didn't satisfy
You put x = 0. It didn't satisfy
You put x = 1. It didn't satisfy
You put x = 4. It satisfied
You put x = 5. It didn't satisfy
You put x = 6. It satisfied

How can you say there is no other value of x that satisfies this equation?
How can you say that all solutions of this equation are included in (C)?



Calm down. Dont get excited.

I meant I plugged in all the values in all the options (a,b,c,d and e)
Option C had two values that satisfy the equations and the other options didnt have two values. So I just went with C and got the correct answer. I did say I got lucky - maybe/maybe not.

"How can you say that all solutions of this equation are included in (C)"

lol Pretty ironic - all solutions

Precisely my point that the wordings of this problem can be easily misinterpreted. Just like you did mine.


The questions at the end 'How can you say...' were for you to mull over, not me pointing fingers. One could read them as 'How can one say ...'
Usually people stay detached and logical on this forum - they don't get excited/irritated so they stay productive.
I guess it's quite easy to misinterpret statements made online. For all the benefits online communication provides, this is certainly a folly it has.

And yes, one does need to read the question very closely to understand the meaning. The question is framed differently, not in the usual 'Which of the following represents all solutions of so and so...'
The word 'includes' helps. Which set "includes" all solutions. So all elements of the set may not be the solution but all solutions need to be in the set!
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Re: Which of the following sets includes ALL of the solutions of  [#permalink]

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New post 19 May 2014, 14:17
Easy. Key points are 2,3,5. Let's try with 6. It works. Only C,D are left. Let's look for a number that can let us choose between these two. How about 8? Doesn't work. Then D is out.

C is the correct answer

Answer: C

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Re: Which of the following sets includes ALL of the solutions of  [#permalink]

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New post 20 May 2014, 06:33
ratinarace wrote:
the equation has 3 intervals 2, 3 , and 5. i.e 4 segments x<2, 2<x<3, 3<x<5, 5<x.

1) When X>5 none of the brackets will change the sign and hence
(x-2)-(x-3) = (x-5)-------> x=6 ..We accept this solution as it satisfies the equation.

Now since we know x=6 is one of the solution we know the answer could be C or D

2) When 3<x<5 here (x-5) will change the sign
(x-2)-(x-3) = -(x-5) ------>x=4 ..We accept the solution as 3<4<5

We can stop solving here as the only set consisting both 6 and 4 is set C hence correct answer is C


Hi,

I have a doubt on this

How can we say X>5 none of the brackets will change the sign and When 3<x<5 here (x-5) will change the sign?

Wat is it to define this?
Please help me in this

Thanks in advance.
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Re: Which of the following sets includes ALL of the solutions of  [#permalink]

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New post 20 May 2014, 07:34
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rrsnathan wrote:
ratinarace wrote:
the equation has 3 intervals 2, 3 , and 5. i.e 4 segments x<2, 2<x<3, 3<x<5, 5<x.

1) When X>5 none of the brackets will change the sign and hence
(x-2)-(x-3) = (x-5)-------> x=6 ..We accept this solution as it satisfies the equation.

Now since we know x=6 is one of the solution we know the answer could be C or D

2) When 3<x<5 here (x-5) will change the sign
(x-2)-(x-3) = -(x-5) ------>x=4 ..We accept the solution as 3<4<5

We can stop solving here as the only set consisting both 6 and 4 is set C hence correct answer is C


Hi,

I have a doubt on this

How can we say X>5 none of the brackets will change the sign and When 3<x<5 here (x-5) will change the sign?

Wat is it to define this?
Please help me in this

Thanks in advance.


Hi rrsnathan,
The eqn :
|x-2|-|x-3|=|x-5|
is about modulus function.

The modulus always takes the magnitude i.e.
|2| = 2 and also |-2| = 2,
so you can see that for negative expression y ; |y | = - (y)
which is same as changing the sign , to make it positive

So,when x>5, all the modulus expression
|x-2|,|x-3|and |x-5| are positive,so we need not change sign

when 3<x<5,
|x-2| is positive , |x-3| is positive and |x-5| is negative,
so we need to change the sign for |x-5| i.e. |x-5| = - (x-5)

That's why the equation
|x-2|-|x-3|=|x-5|
becomes (x-2) -(x-3) = - (x-5) this is what Ratinarace meant, although explained confusingly

Hope above example clears your doubt :)

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Re: Which of the following sets includes ALL of the solutions of  [#permalink]

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New post 17 Jul 2014, 13:18
WholeLottaLove wrote:
Why can we not plug in the answer choices into the question stem to solve that way?



Exactly!! you dont need to solve this one. Just plug in one option from each set and check if it works. Option A and D have 8 so plug it in and check that whether it works. It does not so discard A and D. Option B and E have 5 so plug it in. Again it does work. So we are left with option C. Dont even bother checking if all the values in option C work. Select C and move on.
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Re: Which of the following sets includes ALL of the solutions of  [#permalink]

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New post 17 Jul 2014, 20:22
bhidu wrote:
WholeLottaLove wrote:
Why can we not plug in the answer choices into the question stem to solve that way?



Exactly!! you dont need to solve this one. Just plug in one option from each set and check if it works. Option A and D have 8 so plug it in and check that whether it works. It does not so discard A and D. Option B and E have 5 so plug it in. Again it does work. So we are left with option C. Dont even bother checking if all the values in option C work. Select C and move on.


I don't understand why you chose to ignore options (A) and (D) just because they had a value which is not a solution of x.

Read the question again: Which of the following sets includes ALL of the solutions of x that will satisfy the equation:... ?

This means the option which gives the correct answer "includes" all the solutions of x but it could also have other numbers which are not solutions of x.
The answer is (C) which includes both solutions of x: 4 and 6. But it also has other numbers.

The only way number plugging would work is if you put in every value of (A) - no solutions there. Then check every value of (B) - you get one solution: 4. Now look at the options which have 4. They are (C) and (E). Now check every value of (C). You find that 6 is also a solution. Now see whether (E) has 6. It doesn't. This means option (C) must have all solutions of x since one option has to be correct.
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Re: Which of the following sets includes ALL of the solutions of  [#permalink]

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New post 04 Jun 2018, 03:07
ratinarace wrote:
the equation has 3 intervals 2, 3 , and 5. i.e 4 segments x<2, 2<x<3, 3<x<5, 5<x.

1) When X>5 none of the brackets will change the sign and hence
(x-2)-(x-3) = (x-5)-------> x=6 ..We accept this solution as it satisfies the equation.

Now since we know x=6 is one of the solution we know the answer could be C or D

2) When 3<x<5 here (x-5) will change the sign
(x-2)-(x-3) = -(x-5) ------>x=4 ..We accept the solution as 3<4<5

We can stop solving here as the only set consisting both 6 and 4 is set C hence correct answer is C



Can anyone please explain why we have changed the sign? I am seriously struggling with this issue in most of the similar problems.
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Re: Which of the following sets includes ALL of the solutions of  [#permalink]

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New post 04 Jun 2018, 03:21
ratinarace wrote:

2) When 3<x<5 here (x-5) will change the sign
(x-2)-(x-3) = -(x-5) ------>x=4 ..We accept the solution as 3<4<5

We can stop solving here as the only set consisting both 6 and 4 is set C hence correct answer is C


101mba101 wrote:
Can anyone please explain why we have changed the sign? I am seriously struggling with this issue in most of the similar problems.


The sign change is happening due to the assumed range of x.
As x is assumed to between 3 and 5, exclusive, (i.e. 3 < x < 5) the expression (x - 5) will be negative, as x is less than 5.
For that reason (x - 5) is written as - (x - 5).

Hope this answers your query. :-)


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