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What is the value of |(x+5)/(x+7)|

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What is the value of |(x+5)/(x+7)|  [#permalink]

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New post 19 Aug 2015, 02:49
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What is the value of \(|\frac{(x+5)}{(x+7)}|\)?

(1) \(x^2 + 7x – 18\) = 0

(2) \(3x^2 + 46x + 171\) = 0

Source : Aristotle Prep

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Re: What is the value of |(x+5)/(x+7)|  [#permalink]

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New post 19 Aug 2015, 06:44
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Gnpth wrote:
What is the value of |\(\frac{(x+5)}{(x+7)}\)|?

(1) \(x^2 + 7x – 18\) = 0

(2) \(3x^2 + 46x + 171\) = 0

Source : Aristotle Prep


IMO : B

St 1: \(x^2 + 7x – 18\) = 0

(x+9)(x-2) = 0
Thus x = -9 or x = 2
which gives diff values to (x+5)/(x+7)
Two possible solutions. Hence nt suff

St 2 : \(3x^2 + 46x + 171\) = 0

(3x+19)(x+9) = 0
x=-19/3 or x = -9
(x+5)/(x+7) = 2 for both cases. Hence Sufficient
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Re: What is the value of |(x+5)/(x+7)|  [#permalink]

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New post 19 Aug 2015, 10:17
Can you tell how you got here "(3x+19)(x+9) = 0" without spending too much time?

I got to the part when we know that there are more than one solutions for two, but in order to answer the question I had to find the two solution, wich took me a lot of time.

Thanks.
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What is the value of |(x+5)/(x+7)|  [#permalink]

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New post 19 Aug 2015, 11:41
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Mascarfi wrote:
Can you tell how you got here "(3x+19)(x+9) = 0" without spending too much time?

I got to the part when we know that there are more than one solutions for two, but in order to answer the question I had to find the two solution, wich took me a lot of time.

Thanks.


2 ways:

--- roots of \(ax^2+bx+c = 0\) are , \(x_1\), \(x_2\)= \(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) or

--- you have been given, \(ax^2+bx+c = 0\) ---> \(x_1\) + \(x_2\) (sum of the roots) = -b/a and \(x_1\)*\(x_2\)(product of the roots) = c/a

For this question,

Method 1: \(3x^2+ 46x+171=0\) ---->\(x_1\), \(x_2\)= \(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) = \(\frac{-46\pm\sqrt{46^2-4*3*171}}{2*3}\),

\(x_1\), \(x_2\)= -19/3 or -3.

Method 2: \(x_1\), \(x_2\) = -46/3 and \(x_1\), \(x_2\)=171/3=57

\(x_1\), \(x_2\)= \(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

From this, use the formula \((a-b)^2 = (a+b)^2-4ab\) to calculate a-b and then solve this equation with a+b to get the 2 required values.

Both these methods are lengthy. You should practice more for solving quadratic equations. One way I looked at it was that all 3 coefficients (a,b and c) of the quadratic equation are positive, the 'x' coefficient (i.e. b) could only have been formed by adding 2 positive numbers (as the product of these 2 numbers was positive = 171*3).

Then, I broke down \(3*171\)= \(3^3*19\)and saw that I will 27 and 19 to give me 46 and \(27*19\)= \(171*3\).
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Re: What is the value of |(x+5)/(x+7)|  [#permalink]

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New post 26 Jun 2018, 02:48
If you consider both the equations together we can see that the only value that satisfies both of them is -9.

Now taking both together we get x=-9 and we can find the value of given expression.
The answer should be C not B , if you take the x used everywhere to be the same.

Please let me know the problem in this thought process.
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Re: What is the value of |(x+5)/(x+7)|  [#permalink]

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New post 26 Jun 2018, 03:04
sidsst wrote:
If you consider both the equations together we can see that the only value that satisfies both of them is -9.

Now taking both together we get x=-9 and we can find the value of given expression.
The answer should be C not B , if you take the x used everywhere to be the same.

Please let me know the problem in this thought process.


Hi...

we are looking for the value of \(\frac{|x+5|}{|x+7|}\)..
and from B we get two value of x,,...
x=-19/3..
substitute in \(\frac{|x+5|}{|x+7|}\)=\((|-19/3+5|)/(|-19/3+7|)=|(-4/3)/(2/3)|=2\)
even x=-9 will give you value as 2
so suff

B
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Re: What is the value of |(x+5)/(x+7)|  [#permalink]

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New post 26 Jun 2018, 03:08
I do understand that.

I am saying if we consider both the equations together , both of them will be satisfied with only : x = {-9,2} x= {-9,-19/3} one value of x i.e = -9

And since both the options when taken together give only one value of x , this can be used to find the value of the given expression.
Sorry if i am being very painful :P
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Re: What is the value of |(x+5)/(x+7)|  [#permalink]

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New post 26 Jun 2018, 04:16
sidsst wrote:
I do understand that.

I am saying if we consider both the equations together , both of them will be satisfied with only : x = {-9,2} x= {-9,-19/3} one value of x i.e = -9

And since both the options when taken together give only one value of x , this can be used to find the value of the given expression.
Sorry if i am being very painful :P


Hi sidsst,

In DS question, objective is to get the unique answer. If you get unique answer from statement 1 or Statement 2, or both , or none, it doesn't make any difference. Objective is to get unique answer.
From Statement 1, we are getting two values for equation |(x+5)/(x+7)|- Hence insufficient
but from Statement 2, by putting both the value of x (-19/3 or -9), we are getting unique value of the equation |(x+5)/(x+7)| i.e. 2 - Therefore Sufficient.

Hence, answer is B i.e statement 2 is sufficient to answer.
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Re: What is the value of |(x+5)/(x+7)|  [#permalink]

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New post 26 Jun 2018, 11:30
sidsst wrote:
I do understand that.

I am saying if we consider both the equations together , both of them will be satisfied with only : x = {-9,2} x= {-9,-19/3} one value of x i.e = -9

And since both the options when taken together give only one value of x , this can be used to find the value of the given expression.
Sorry if i am being very painful :P


Hello

A basic rule of DS is the following:

Combine the two statements ONLY if none of the two statements is sufficient to answer the question on its own.
Re: What is the value of |(x+5)/(x+7)| &nbs [#permalink] 26 Jun 2018, 11:30
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