Here's one approach.....

Key concept: \((x^n)(y^n) = (xy)^n\)

Given:
Quantity A: \(5^x +1\)
Quantity B: \(6^x\)

Subtract \(5^x\) from both quantities to get:
Quantity A: \(1\)
Quantity B: \(6^x - 5^x\)

Applied the key concept above to factor 5^x out of Quantity B to get:
Quantity A: \(1\)
Quantity B: \(5^x(1.2^x - 1)\)

At this point we can apply a little bit of number sense...
Since \(x>1\), we know that \(5^x\) is greater than 5
Since \(x>1\), we know that \(1.2^x\) is greater than 1.2, which means \(1.2^x - 1\) is greater than 0.2

So Quantity B becomes:
Quantity A: \(1\)
Quantity B: (some number greater than 5)(some number greater than 0.2)

We know that \((5)(0.2) = 1\), so when we simplify Quantity B we get:
Quantity A: \(1\)
Quantity B: some product greater than 1

Answer: B

RELATED VIDEO FROM OUR COURSE