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What is the value of x?

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What is the value of x?  [#permalink]

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New post 25 Jun 2014, 09:26
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What is the value of x?

(1) |x+5|=|x+3|
(2) |x+3|=1
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What is the value of x?  [#permalink]

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New post 25 Jun 2014, 09:30
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Re: What is the value of x?  [#permalink]

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New post 25 Jun 2014, 13:00
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goodyear2013 wrote:
What is the value of x?

(1) |x+5|=|x+3|
(2) |x+3|=1


we can also use the number line to calculate the value of x

st.1 for x<-5, and x>-3 we have now possible solution.
but for -5<x<-3, we have
|x+5|=x+5 and |x+3|= -x-3

thus we have x+5=-x-3; 2x=-8, x= -4. hence sufficient

st.2

when x>-3
x+3=1 and x=-2 which is a valid solution
and when x<-3 we have
-x-3=1
x = -4 which is also a valid solution.
hence statement 2 alone is not sufficient

therefore A
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Re: What is the value of x?  [#permalink]

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New post 18 Jul 2017, 04:11
Bunuel wrote:
What is the value of x?

(1) \(|x+5| = |x+3|\) --> square both sides: \((x+5)^2=(x+3)^2\) --> \(x^2+10 x+25 = x^2+6 x+9\) --> \(4x=-16\) --> \(x=-4\). Sufficient.

(2) \(|x+3| = 1\) --> x + 3 = 1 or x + 3 = -1. Hence, x = -2 or x = -4. Not sufficient.

Answer: A.




Hi Bunuel,

I got the answer A but just by plugging in numbers. I looked at the problem and saw that in order for |x+5| = |x+3| the difference has to be 2. Therefore |-1| = |1|.

|x+5| = 1, x = -4 or -6
|x+3| = 1, x = -4 or -2

We have one answer that fits both, therefore sufficient.
I had the same reasoning as you for statement (2).

Answer. A

Am I correct in my reasoning? I wouldn't have considered squaring both sides as it's not something I've been taught before. Is this just something people know to do?
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Re: What is the value of x?  [#permalink]

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New post 18 Jul 2017, 04:37
goodyear2013 wrote:
What is the value of x?

(1) |x+5|=|x+3|
(2) |x+3|=1





Stmt 1)
Three cases can be considered
i) x+5 = x+3 -> No x value can be derived
ii)x+5 = -(x+3) -> x=-4
iii)-(x+5) = x+3 -> x=-4

Hence suff

Stmt 2)
x+3=1 -> x=-2
x+3=-1 -> x=-4
2 values, hence insuff

Answer A
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Re: What is the value of x?  [#permalink]

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New post 18 Jul 2017, 08:19
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tommh wrote:
Bunuel wrote:
What is the value of x?

(1) \(|x+5| = |x+3|\) --> square both sides: \((x+5)^2=(x+3)^2\) --> \(x^2+10 x+25 = x^2+6 x+9\) --> \(4x=-16\) --> \(x=-4\). Sufficient.

(2) \(|x+3| = 1\) --> x + 3 = 1 or x + 3 = -1. Hence, x = -2 or x = -4. Not sufficient.

Answer: A.




Hi Bunuel,

I got the answer A but just by plugging in numbers. I looked at the problem and saw that in order for |x+5| = |x+3| the difference has to be 2. Therefore |-1| = |1|.

|x+5| = 1, x = -4 or -6
|x+3| = 1, x = -4 or -2

We have one answer that fits both, therefore sufficient.
I had the same reasoning as you for statement (2).

Answer. A

Am I correct in my reasoning? I wouldn't have considered squaring both sides as it's not something I've been taught before. Is this just something people know to do?


Hi tommh,

Quote:
I wouldn't have considered squaring both sides as it's not something I've been taught before. Is this just something people know to do?


Yes, this is a standard method to solve such questions.

You can also solve this question using the modulus/absolute value definition.

Definition: Absolute value of a number is distance from 0.

Example: |x| = 3, we can write it as |x-0| = 3. x: those points whose distance from 0 is 3. So, on number line two points will satisfy the condition => x = -3 or 3

---------- -3-------------0-------------3--------------

Example2. |x+3| = 3, we can write it as |x- (-3)| = 3. x: those points whose distance from (-3) is 3 units => x = -6 or 0. Refer: (Example2.jpg)


Now, back to the question.

St.1: |x+5| = |x+3| . This can be written as |x - (-5)| = |x - (-3)|. x is number which is equidistant from (-5) and (-3). => x = -4. No other value will satisfy this condition. Please refer attached diagram (Statement1.jpg) . Hence, sufficient.

St2: |x+3| = 1. |x - (-3)| = 1 => x = -2 or -4. Not sufficient.

Hope it helps.

Thanks.
Attachments

Statement1.jpg
Statement1.jpg [ 102.57 KiB | Viewed 741 times ]

Example2.jpg
Example2.jpg [ 78.57 KiB | Viewed 740 times ]

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Re: What is the value of x?  [#permalink]

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New post 18 Jul 2017, 12:05
Thank you ganand, that makes sense.
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Re: What is the value of x?  [#permalink]

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New post 28 Jul 2017, 13:59
Value of X?
1) from this we get - 4 (keeping LHS and RHS negative and then reversing the same).
Substituting x has a constant value --> |-4 +5| =1 and |-4 +3|=1
SUFF (A)

2) |x+3|= 1
x= 4 and x= -4
substituting: |4+3| = 1 but not equal to 7 and |-4 +3| =1 so we have two values. Not suff.
Ans: A
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Re: What is the value of x?  [#permalink]

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New post 30 Jul 2017, 17:23
goodyear2013 wrote:
What is the value of x?

(1) |x+5|=|x+3|
(2) |x+3|=1


We need to determine the value of x.

Statement One Alone:

|x+5|=|x+3|

Since the two absolute value expressions are equal, we can solve for each situation: (1) when they are both positive and (2) when they have opposite signs.

(1) Both positive:

x + 5 = x + 3

We see that we do not get an answer for x.

(2) Opposite signs:

-(x + 5) = x + 3

-x - 5 = x + 3

-8 = 2x

-4 = x

We see x = -4. Statement one alone is sufficient to answer the question.

Statement Two Alone:

|x+3|=1

We can solve for each situation: (1) when (x + 3) is positive and (2) when (x + 3) is negative.

(1) (x + 3) is positive:

x + 3 = 1

x = -2

(2) (x + 3) is negative:

-x - 3 = 1

-x = 4

x = -4

We cannot determine a unique value for x.

Answer: A
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Re: What is the value of x?   [#permalink] 30 Jul 2017, 17:23
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