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13 Feb 2017, 03:16
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
75% (01:16) correct
25%
(01:47)
wrong
based on 916
sessions
History
Date
Time
Result
Not Attempted Yet
\(7^3 + 21^3 =\)
A. \(7^4*2^2\)
B. \(7^3*2^4\)
C. \(7^3*3^3\)
D. \(7^3*3^4\)
E. \(7^4*3^3\)
A. \(7^4*2^2\)
B. \(7^3*2^4\)
C. \(7^3*3^3\)
D. \(7^3*3^4\)
E. \(7^4*3^3\)
13 Feb 2017, 03:56
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7^3+21^3
7^3 + 7^3*3^3 => 7^3(1+3^3)= 7^3*28=7^3*7*4= 7^4*2^2
answer is a
7^3 + 7^3*3^3 => 7^3(1+3^3)= 7^3*28=7^3*7*4= 7^4*2^2
answer is a
15 Feb 2017, 09:06
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Bunuel
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 even
So, 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 = ????4
Now we'll check the remaining answer choices to see which one yields an answer with units digit 4
A. \(7^4 * 2^2\)
\(7^4\) = (7)(7)(7)(7) = ????1 [some number with units digit 1]
\(2^2\) = (2)(2) = 4
So, \(7^4 * 2^2\) = (????1)(4) = ??????4
Great - keep A
B. \(7^3*2^4\)
\(7^3\) = (7)(7)(7) = ????3
\(2^2\) = (2)(2)(2)(2) = 16
So, \(7^3 * 2^4\) = (????3)(16) = ??????8
ELIMINATE B
Answer: A
