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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: \(\frac{b}{c} = \frac{(a+b)^2}{a^2+2ab+b^2} - 1\) \(\frac{b}{c} = \frac{(a+b)^2}{(a+b)^2} - 1\) \(\frac{b}{c} = 1 - 1 = 0\) \(b = 0\)

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.

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.
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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
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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

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).