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--> -(3x-7)=2x+2 on solving this we get x=1 --> +(3x-7)=2x+2 on solving this we get x=9 so insufficient

B ) x^2=9x x^2-9x=0 x(x-9)=0 hence x=0,9 insuff

combining both will give x=9 hence sqroot(9) will give 3 which is a prime number

OA is C. I was wondering whether we should consider negative values. Sq root of 9 = +/-3. +3 is prime and -3 is not. What do you say?
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|3x-7| = 2x +2. here L.H.S is positive so 2x+2 >= 0---> 2x>=-2--> x>=-1

so if if x>= -1 then |3x-7| = -3x+7 = 2x+2

-5x = -5 x = 1

only 1 value so sufficient. Ans A ( my question is why we are considering other scenario to get 9)

in st2

x^2 = 9x x^2-9x = 0 x(x-9) = 0 x= 0 or 9

here we are getting 2 values so not sufficient.

2 questions:

1. Does x=9 satisfy the equation? 2. Why do you say that when x>=-1, then |3x-7| = -(3x-7)?

Hi Bunnel,

1. Yes x=9 satisfy the equation. 2. I told x>= -1 because in st1 it is given that |3x-7| = 2x+2. Here LHS. is in modulus so it is >=0. so RHS should be >=0 2x+2>= 0 --> 2x>=-2-->x>=-1

|3x-7| = 2x +2. here L.H.S is positive so 2x+2 >= 0---> 2x>=-2--> x>=-1

so if if x>= -1 then |3x-7| = -3x+7 = 2x+2

-5x = -5 x = 1

only 1 value so sufficient. Ans A ( my question is why we are considering other scenario to get 9)

in st2

x^2 = 9x x^2-9x = 0 x(x-9) = 0 x= 0 or 9

here we are getting 2 values so not sufficient.

2 questions:

1. Does x=9 satisfy the equation? 2. Why do you say that when x>=-1, then |3x-7| = -(3x-7)?

Hi Bunnel,

1. Yes x=9 satisfy the equation. 2. I told x>= -1 because in st1 it is given that |3x-7| = 2x+2. Here LHS. is in modulus so it is >=0. so RHS should be >=0 2x+2>= 0 --> 2x>=-2-->x>=-1

Thanks

You did not understand my second question. Yes, from (1) x>=-1 BUT why does that mean that |3x-7| = -(3x-7)?

Hey Bunuel I know I was using Bunnel bcz in my area where I live in india its mean wise. So I used this word for you.

i think i got confusion here |3x-7| = -(3x-7) as i thought putting -1 makes it negative in modulus |-3-7| . but I think this is not the case and it should be |3x-7| = 3x-7.

Thanks Bunuel for all your replies. Please clarify this

Hey Bunuel I know I was using Bunnel bcz in my area where I live in india its mean wise. So I used this word for you.

i think i got confusion here |3x-7| = -(3x-7) as i thought putting -1 makes it negative in modulus |-3-7| . but I think this is not the case and it should be |3x-7| = 3x-7.

Thanks Bunuel for all your replies. Please clarify this

That's not correct.

|3x-7| = 3x-7, when x > 7/3. |3x-7| = -(3x-7), when x <= 7/3.

x>=-1 is not sufficient info to say whether |3x-7| = 3x-7 or |3x-7| = -(3x-7). For example, if x=0<7/3, then |3x-7| = -(3x-7) but if x=100>7/3, then |3x-7| = 3x-7.

Hey bunuel, In Manhattan gmat book its written that absolute values have +ve or -ve value. For +ve value the sign after solving is positive then its a correct soln, same goes for -ve. But here when we solve for +ve value we get +9, thats a correct soln, but for -ve soln we get +1, which isnt negative, so its not a legitimte soln and hence should be ignored, acc to MGMAT. Plz help !

Hey bunuel, In Manhattan gmat book its written that absolute values have +ve or -ve value. For +ve value the sign after solving is positive then its a correct soln, same goes for -ve. But here when we solve for +ve value we get +9, thats a correct soln, but for -ve soln we get +1, which isnt negative, so its not a legitimte soln and hence should be ignored, acc to MGMAT. Plz help !

Not sure I understand what you mean there.

As for the roots of |3x - 7| = 2x + 2: both x = 1 and x = 9 satisfy this equation, thus both are valid solutions.

Maybe if you could show your work, I'd be able to say more.
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