Which of the following represents the average of \(11^{61}\) and \(11^{63}?\)

[Gmat_mission]

Which of the following represents the average of \(11^{61}\) and \(11^{63}?\)

A. \(11^{31}\)
B. \(11^{62}\)
C. \(61\cdot 11^{61}\)
D. \(62\cdot 11^{62}\)
E. \(63\cdot 11^{63}\)

Answer: C

Source: Veritas Prep

[Brent@GMATPrepNow]

Which of the following represents the average of \(11^{61}\) and \(11^{63}?\)

A. \(11^{31}\)
B. \(11^{62}\)
C. \(61\cdot 11^{61}\)
D. \(62\cdot 11^{62}\)
E. \(63\cdot 11^{63}\)

Answer: C

Source: Veritas Prep

Average = (11^61 + 11^63)/2

Let's simplify: (11^61 + 11^63)
Factor to get: 11^61(1 + 11^2)
Evaluate to get: 11^61(1 + 121)
Simplify: 11^61(122)

So the average = (11^61 + 11^63)/2 = (11^61)(122)/2 = (11^61)(61)

Answer: C