Bunuel wrote:

\(7^3 + 21^3 =\)

A. \(7^4 * 2^2\)

B. \(7^3*2^4\)

C. \(7^3*3^3\)

D. \(7^3*3^4\)

E. \(7^4*3^3\)

This question can also be solved without using any exponent laws.

First, we'll use the fact that

the product of a bunch of odd integers will always be odd. And we'll use the fact that,

if a product contains 1 or more even integers, then that product will be evenSo, 7³ + 21³ = (some odd number)³ + (some odd number)³

= ODD + ODD

= EVEN

So, 7³ + 21³ = an even number

Now check the answer choices....

A. \(7^4 * 2^2\) = \(ODD^4*EVEN^2\) = ODD * EVEN = EVEN (Keep)

B. \(7^3*2^4\) = \(ODD^3*EVEN^4\) = ODD * EVEN = EVEN (Keep)

C. \(7^3*3^3\) = \(ODD^3 * ODD^3\) = ODD * ODD = ODD (eliminate)

D. \(7^3*3^4\) = \(ODD^3 * ODD^4\) = ODD * ODD = ODD (eliminate)

E. \(7^4*3^3\) = \(ODD^4 * ODD^3\) = ODD * ODD = ODD (eliminate)

So, the correct answer is A or B

At this point, let's focus on the UNITS DIGITS ONLY

\(7^3\) = (7)(7)(7) = ????

3 [some number with units digit 3]\(21^3 =\) (21)(21)(21) = ????

1 [some number with units digit 1] So, \(7^3 + 21^3 =\) ????

3 + ????

1 = ????

4Now we'll check the remaining answer choices to see which one yields an answer with units digit

4A. \(7^4 * 2^2\)

\(7^4\) = (7)(7)(7)(7) = ????

1 [some number with units digit 1]\(2^2\) = (2)(2) =

4So, \(7^4 * 2^2\) = (????

1)(

4) = ??????

4Great - keep A

B. \(7^3*2^4\)

\(7^3\) = (7)(7)(7) = ????

3\(2^2\) = (2)(2)(2)(2) = 1

6So, \(7^3 * 2^4\) = (????

3)(1

6) = ??????

8ELIMINATE B

Answer: A

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Brent Hanneson – GMATPrepNow.com