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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