Problem Solving

5^12 + 5^13 =
(A) 5^25
(B) 10^25
(C) 6(5^12 )
(D) 10^12 + 5
(E) 2(5^12 ) + 5

OA is C

5^12 + 5^13
Factor out a 5^12:
5^12(1 + 5) = 6(5^12)
Choose C.

truplayer256 wrote:5^12 + 5^13
Factor out a 5^12:
5^12(1 + 5) = 6(5^12)
Choose C.

Great job!

Here's a bit of clarification on solving this type of problem.

There are simple rules for multiplying exponents (x^a * x^b = x^(a+b)) and raising exponents to other exponents ((x^a)^b=x^(a*b)), but there's no simple way to add or subtract exponents.

In fact, the only time you can add or subtract exponents is when both the base and the power are identical.

For example, there's no easy way to solve x^4 + 3x^3; however, when the base and exponent are identical, you simply add the coefficients, as in:

3(x^4) + 4(x^4) = 7(x^4)

So, if you want to solve, you need to coordinate the base and the power.

We do so by factoring out the powers we don't want (using the multiplication of exponents rule); on the GMAT, that pretty much always means leaving the smaller exponent as is and reducing the larger one.

In this problem, we have 5^12 and 5^13; so, we leave 5^12 as is and factor out 5^12 from the 5^13 term, as follows:

5^12 + 5^13
= 5^12 + (5^1)(5^12)
= 1(5^12) + 5(5^12)
= 6(5^12)

done!