soloyolodolo wrote:
I agree with your explanation of the answer, however based on GMAT rules. I think answer would be D?
Maybe someone else can help. I know there are numerous people in the forums who are much more intelligent and math wizards.
Till the time someone else pitches in, inline is the
Official Explanation Statement (1) gives you that \((3^a)(3^b)=81\)
Remember that to find the product of two exponential expressions with a common base, you simply add their exponents.
That means that \((3^a)(3^b)=81\) becomes 3^(a+b)=81
The right side of the equation can then be rewritten as \(3^4\) giving you the equation 3^(a+b) = \(3^4\)
so a+b=4
You can therefore conclude that statement (1) is sufficient when taken on its own.
Statement (2) gives that \((3^a)(5^b)=225\)
If you factor 225, it becomes \((3^2)(5^2)=(3^a)(5^b)\), At this point, it is tempting to say that a+b=4
But remember -- you haven’t been told even whether a and b are integers.
It is possible to say that a=4 and that b is equal to an irrational number (log5 \(\frac{225}{81}\), if you do the math).
Because the equation could yield multiple values of a and b
You must conclude that statement (2) is insufficient and choose answer choice (A).
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Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.