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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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19 Aug 2015, 01:49
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Difficulty:

95% (hard)

Question Stats:

30% (02:21) correct 70% (02:43) wrong based on 133 sessions

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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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19 Aug 2015, 05:44
1
1
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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19 Aug 2015, 09:17
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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19 Aug 2015, 10:41
1
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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26 Jun 2018, 01:48
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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26 Jun 2018, 02:04
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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26 Jun 2018, 02:08
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
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Re: What is the value of |(x+5)/(x+7)|  [#permalink]

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26 Jun 2018, 03:16
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

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.

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

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26 Jun 2018, 10:30
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

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, 10:30
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