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Hi. From S1 we see that a is either 0 or 2. Insufficient. S2. You have to notice that we need to simplify the fraction in S2: \frac{b}{c} = \frac{(a+b)^2}{a^2+2ab+b^2} - 1 \frac{b}{c} = \frac{(a+b)^2}{(a+b)^2} - 1 \frac{b}{c} = 1 - 1 = 0 b = 0

Enough solution has been given from the previous posts. (1) a= 0 or 2...insufficient (2) b=0...sufficient to answer whether abc = 0 (yes). B, off course is the answer. _________________

KUDOS me if you feel my contribution has helped you.

\frac{b}{c} = \frac{(a+b)^2}{a^2+2ab+b^2} - 1 ( a \ne -b and c \ne 0 ) (a+b)^2=a^2+2ab+b^2 therefore frac{(a+b)^2}{a^2+2ab+b^2}=1 \frac{(a+b)^2}{a^2+2ab+b^2} - 1 =0 so 2 is sufficient so Answer=B _________________

As we know a^2 + 2ab +b^2 is(a+b)^2 Therefore the expression (a+b)^2/(a^2 +2ab + b^2) can be reduced to 1 So substituting this in our equation we get b/c=1 - 1 =0 which implies b=0, which satisfies our condition

Can't seem to figure out the explanation that I saw on the test.

Thanks, John.

BELOW IS REVISED VERSION OF THIS QUESTION:

Is abc = 0 ?

In order abc = 0 to be true at least one of the unknowns must be zero.

(1) a^2 = 2a --> a^2-2a=0 --> a(a-2)=0 --> a=0 or a=2. If a=0 then the answer is YES but if a=2 then abc may not be equal to zero (for example consider: a=2, b=3 and c=4). Not sufficient.

(2) b= \frac{(a*\sqrt{c}+b*\sqrt{c})^2}{a^2+2ab+b^2} - c --> b= \frac{c*(a+b)^2}{(a+b)^2} - c --> b=c-c --> b=0. Sufficient.

Is this the right simplification for statement 1:-

I got only 1 value for a i.e. a=2

a square = 2a a * a = 2a a = 2

if its not correct simplification please explain, why?

Yes, that's not correct.

Never reduce an equation by a variable (or expression with a variable), if you are not certain that the variable (or the expression with a variable) doesn't equal to zero. We can not divide by zero.

So, if you divide (reduce) a^2=a by a you assume, with no ground for it, that a does not equal to zero thus exclude a possible solution (notice that both a=2 AND a=0 satisfy the equation).

Is this the right simplification for statement 1:-

I got only 1 value for a i.e. a=2

a square = 2a a * a = 2a a = 2

if its not correct simplification please explain, why?

Yes, that's not correct.

Never reduce an equation by a variable (or expression with a variable), if you are not certain that the variable (or the expression with a variable) doesn't equal to zero. We can not divide by zero.

So, if you divide (reduce) a^2=a by a you assume, with no ground for it, that a does not equal to zero thus exclude a possible solution (notice that both a=2 AND a=0 satisfy the equation).