If x = (9b - 3ab)/(3/a - a/3), what is x? (1) 9ab/(3+a) = 18/5 (2) b

Question

If  x = \frac{9b - 3ab}{\frac{3}{a} - \frac{a}{3}} , what is x?

(1)  \frac{9ab}{3+a} = \frac{18}{5}

(2)  b = 1

Nidzo · Answer

1) Looking at the top line alone:  9ab = 18  tells us that either one of  a  or  b  is  2  and the other is  1 .
 Looking at the bottom line:  3+a = 5  tells us that  a = 2 , and therefore  b = 1

SUFFICIENT

2) Only gives us the value of  b , and we cannot deduce  a  from this.

INSUFFICIENT

Answer A

Crytiocanalyst · Answer

THrough simplification we get 3b* (3-a) * 3a / 3-a * 3+a

=>9ab/ 3-a 
Clearly A is sufficient we cannot sovle with B since 2 variables cannot be solved in 1 equation

Therefore IMO A

starredastro · Answer

Your answer is correct ,  but your approach is incorrect .
Why are you assuming that a and b are integers?
 If you simplify the equation using the (a^2-b^2) = (a-b)(a+b) formula in the denominator, after applying the LCM you will get the exact expression mentioned in statement (1).  
 Hence, option A is sufficient alone to answer the target question!

Namangupta1997 · Answer

Hi  chetan2u   Bunuel

Why are we not considering the fact that "a" cannot be equal to +-3 as (9-a^2) is in denominator ? If we use b=1, it ensures that the a =2, and hence removes the possibility of "a" being +-3. Why isn't the correct answer C ? Using the equation in statement 1, we just get x = 18(3-a)/5(3-a) which would be equal to 18/5 IF it was mentioned a is not equal to 3.

What am I missing ? Please clarify.

chetan2u · Answer

Statement I should tell you that the initial equation requires to be simplified to check statement I.

x = \frac{9b - 3ab}{\frac{3}{a} - \frac{a}{3}}

x = \frac{9b - 3ab}{\frac{9-a^2}{3a}}

x=\frac{3a(9b-3ab)}{9-a^2}

x=\frac{3a*3b(3-a)}{(3-a)(3+a)}=\frac{9ab}{3+a}

Statement I gives this value as 18/5.
Sufficient

Statement II gives b=1
So,  x=\frac{9*a*1}{3+a}=\frac{9a}{3+a} 
x depends on a.
If a is 1, x is 9/4
If a is 2, x is 18/5
If a is 3, x is 27/6 or 9/2 and so on
Insufficient

A

bumpbot · Answer

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If x = (9b - 3ab)/(3/a - a/3), what is x? (1) 9ab/(3+a) = 18/5 (2) b

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If x = (9b - 3ab)/(3/a - a/3), what is x? (1) 9ab/(3+a) = 18/5 (2) b

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