DOUBT IN MANHATTAN QUANT QUESTION

[A aryan0406]

If x = (9b - 3ab)/(3/a - a/3), what is x?

(1) 9ab/(3+a) = 18/5
(2) b = 1


This question is present in Manhattan guide 2 in chapter Strategy:Combos.
It's official answer is A. However I have doubt in that.
In the official Manhattan guide explanation the equation is reformed into 3a(3b)(3-a)/(3-a)(3+a)) and then (3-a) is cancelled from top and the bottom.

However according to rules we can only cut some variables from numerator and denominator only when we are sure that they are not equal to zero. But here it is possible that (3-a) can be equal to 0. When I take a=3 and b=4/5 the equation 9ab/(3+a) = 18/5 is satisfied but now (3-a) cannot be cancelled from numerator and denominator.

If the second option b=1 is taken into consideration than it can be proved that a is never equal to 3 by substituting in the statement (1) equation.
So shouldn't the answer be "C" because both the statements are required to give an unambiguous answer?

For answer to be "A" it should be specified in the question that a is not equal to 3.

[G gmatbyexample]

If x = (9b - 3ab)/(3/a - a/3), what is x?

(1) 9ab/(3+a) = 18/5
(2) b = 1


This question is present in Manhattan guide 2 in chapter Strategy:Combos.
It's official answer is A. However I have doubt in that.
In the official Manhattan guide explanation the equation is reformed into 3a(3b)(3-a)/(3-a)(3+a)) and then (3-a) is cancelled from top and the bottom.

However according to rules we can only cut some variables from numerator and denominator only when we are sure that they are not equal to zero. But here it is possible that (3-a) can be equal to 0. When I take a=3 and b=4/5 the equation 9ab/(3+a) = 18/5 is satisfied but now (3-a) cannot be cancelled from numerator and denominator.

If the second option b=1 is taken into consideration than it can be proved that a is never equal to 3 by substituting in the statement (1) equation.
So shouldn't the answer be "C" because both the statements are required to give an unambiguous answer?

For answer to be "A" it should be specified in the question that a is not equal to 3.

Your analysis is good, however there is an implicit assumption here which I feel you may be missing.

x is given to be a quantity (expressed in RHS with a and b as variables). In GMAT, it is safe to assume that any given quantity will not be zero/zero (undefined). Basically by providing x = {expression} the question is implicitly saying that in the RHS there is not a 0/0 situation and hence the solution takes that implicit assumption and goes from there.

Does that help?