nsamkari wrote:Dear gmatguruny,
how is it come that doesn't matter if the exponent of 4 is different than 11 and the most important part is 5^21!!!!!
could you clarify please?
5²¹ * 4¹¹ = 2 * 2^n *
5^n.
It is given that the LHS is equal to the RHS.
Thus, if the LHS has a prime number raised to a power, then the RHS must include the SAME PRIME NUMBER raised to the SAME POWER.
Since the LHS has 5²¹, the RHS must also have 5²¹.
Thus, on the RHS, 5^n = 5²¹.
n=21.
No need to do any more work.
For the skeptical, here's the full algebraic solution:
5²¹ * 4¹¹ = 2 * (10)^n.
5²¹ * 4¹¹ = 2 * (2*5)^n.
5²¹ *
4¹¹ =
2 * 2^n * 5^n
5²¹ *
(2²)¹¹ =
2^(n+1) * 5^n
5²¹ *
2²² =
2^(n+1) * 5^n.
The LHS has 2²².
Thus, on the right hand side:
2^(n+1) = 2²²
n=21.
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