Harshgmat wrote:

If \(a\) and \(b\) are both positive integers greater than 1 and \(a^b\) = \(a^{(11b - 60)}\), what is the value of \(a*b\) ?

(1) \(a^ 2 = 7|a|\)

(2) \(|a| = 7\)

Here is my take on this question.

Given \(a^b\) = \(a^{(11b - 60)}\)

b=11 b - 60

b=6

Now the question becomes a*6 = ?

1) \(a^ 2 = 7|a|\)

\(a^ 4 - 49 a^2 = 0\)

\(a^ 2(a^2 - 49) = 0\)

Solving which will give value of a as a= 0, 7 and -7

But since it is given that a is a positive number we can ignore -42 and 0, giving us the answer as 42.

Which is sufficient by its own.

2) \(|a| = 7\)

will give value of a as 7 and -7

Here we will get multiple values of a*6 = 42 or -42

But since it is given that a is a positive number we can ignore -42, giving us the answer as 42.

Which is sufficient by its own.

Giving the final answer as

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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.

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