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

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

#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

(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

(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)

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.

The answer is therefore B.

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

The answer is B.

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