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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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15 Dec 2019, 22:31
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30% (02:36) correct 70% (02:41) wrong based on 44 sessions

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What is the value of $$|\frac{x+5}{x+7}|$$?

(1) $$x^2 + 7x – 18 = 0$$

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

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

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15 Dec 2019, 22:53
To get the value of absolute value equation in the question, we need the value of x.

Let's evaluate the statements.

a.
x^2 + 7x - 18 = 0
x^2 + 9x - 2x - 18 = 0
x(x+9) - 2(x+9) = 0
(x+9)(x-2) = 0
x = -9 or x = 2

When you put above value in the absolute value equation, 2 different answers come. So, statement a is not sufficient.

b.
3x^2 + 46x + 171 = 0
3x^2 + 27x + 19x + 171 = 0
3x(x+9) + 19 (x+9) = 0
(3x+19)(x+9) = 0
x = -19/3 or x = -9

Putting both values of x in the absolute value equation, we get 2 different answers. So, statement 2 is not sufficient.

Combining both statements, we can see that common value of x is -9. Hence, answer is C.
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Re: What is the value of |(x + 5)/(x + 7)| ?  [#permalink]

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15 Dec 2019, 23:08
Statement 1: $$x^2 + 7x – 18 = 0$$
$$x^2 + 9x - 2x – 18 = 0$$ (Easy to break)
x(x+9) -2(x+9) = 0
(x+9)(x-2) = 0
x= -9 and 2 (2 different values - Not Sufficient)

A D / B C E

Statement 2: $$3x^2 + 46x + 171 = 0$$
I followed the formula approach because I was unable to break spontaneously : $$x = (−b + √(b^2 − 4ac))/2a$$ , $$x = (−b - √(b^2 − 4ac))/2a$$
$$x = (−46 + √(46^2 − 4*3*171))/2*3$$ , $$x = ((−46 + √(46^2 − 4*3*171))/2*3$$
Solving will get: -19/3 and -9 (2 different values - Not Sufficient)

A D / B C E

Combining both statements and we get only 1 common solution '-9'. Hence 'C' is the Winner
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Re: What is the value of |(x + 5)/(x + 7)| ?  [#permalink]

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15 Dec 2019, 23:40
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I am pretty sure lot of us would look at two values from each and then find common values from both and mark C.
But always check back after putting the values to get to your answer.

You will go WRONG if you are looking for value of x, but if you realize that you are looking for the value of $$|\frac{x+5}{x+7}|$$, you will be correct..

What is the value of $$|\frac{x+5}{x+7}|$$?

(1) $$x^2 + 7x – 18 = 0......x^2+9x-2x-18=0......(x+9)(x-2)=0$$
So, x can be -9 or 2 and
$$|\frac{x+5}{x+7}|$$=$$|\frac{-9+5}{-9+7}|=\frac{-4}{-2}=2$$..
$$|\frac{x+5}{x+7}|$$=$$|\frac{2+5}{2+7}|=\frac{7}{9}$$
Two different values
Insuff

(2) $$3x^2 + 46x + 171 = 0..........3x^2+27x+19x+171=3x(x+9)+19(x+9)=0.......(x+9)(3x+19)=0.$$
So, x can be -9 or -19/3 and
$$|\frac{x+5}{x+7}|$$=$$|\frac{-9+5}{-9+7}|=\frac{-4}{-2}=2$$..
$$|\frac{x+5}{x+7}|$$=$$|\frac{\frac{-19}{3}+5}{\frac{-19}{3}+7}|=|\frac{-19+15}{-19+21}|=|\frac{-4}{2}|=2$$
Suff

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

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16 Dec 2019, 01:28
1
#1
x2+7x–18=0
we get value of x = -9 and +2
and 2 different values of |x+5/x+7|
insufficient
#2
3x2+46x+171=0
solving we get value of x = -9 and -19/3
using which we get |x+5/x+7| = 2 ; sufficient
IMO B

What is the value of|x+5/x+7|?

(1) x2+7x–18=0

(2) 3x2+46x+171=0
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Re: What is the value of |(x + 5)/(x + 7)| ?  [#permalink]

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16 Dec 2019, 02:26
(1) x2+7x–18=0 ....... will have 2 values for x.....Insufficient

2) 3x2+46x+171=0......will have 2 values for x.....Insufficient

combing both we get single value for x....sufficient

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

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Updated on: 17 Dec 2019, 02:06
Quote:
What is the value of |x+5/x+7|?

(1) x^2+7x–18=0

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

(1) x^2+7x–18=0 insufic

$$x^2+7x–18=0…(x+9)(x-2)=0…x=(-9,2)$$

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

Ans (B)

Originally posted by exc4libur on 16 Dec 2019, 04:31.
Last edited by exc4libur on 17 Dec 2019, 02:06, edited 2 times in total.
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Re: What is the value of |(x + 5)/(x + 7)| ?  [#permalink]

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16 Dec 2019, 06:19
1
What is the value of |x+5|/|x+7|?

1. x^2+7x-18=0
x^2+7x-18=0
(x+9)(x-2)=0
x=-9, or x=2

when x=-9, we have (|-4|)/(|-2|)=2
when x=2, we have (|7|)/(|9|)=7/9.
Since we don't have different values for the given expression corresponding to x=-9 and x=2, statement 1 is not sufficient.

2: 3x^2+46x+171=0
3x^2+46x=-171
(x+23/3)^2=529/9-513/9
(x+23/3)=+-4/3
Hence x=-9, or x=-19/3

When x=-9, (|-4/-2|)=2
when x=-19/3, we have |((15/3-19/3)/(21/3-19/3))| = |((-4/3)/(2/3))|=|-2| = 2.
Since the expression yields the same value of 2 when x=-9 and when x=-19/3, statement 2 is sufficient.

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

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16 Dec 2019, 12:32
1
What is the value of $$|\frac{x+5}{x+7}|$$ ?

(Statement1) $$x^{2}+7x–18=0$$
--> (x-2)*(x+9) =0
if x=2, then $$|\frac{x+5}{x+7}| = \frac{7}{9}$$
if x=-9, then $$|\frac{x+5}{x+7}| = 2$$
--> Two values. Clearly insufficient

(Statement2) $$3x^{2}+46x+171=0$$ (171 =3*3*19)
--> (3x+19)*(x+9)=0
if $$x=-\frac{19}{3}$$, then $$|\frac{x+5}{x+7}|= |(-\frac{19}{3}+5)/(-\frac{19}{3}+7)|= |(-\frac{4}{3})/(\frac{2}{3})|= 2$$

if x= -9, then $$|\frac{x+5}{x+7}| =| \frac{(-9+5)}{(-9+7)}|= 2$$

Both of them are the same value.
Sufficient

Re: What is the value of |(x + 5)/(x + 7)| ?   [#permalink] 16 Dec 2019, 12:32
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