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7^3 + 21^3 =

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7^3 + 21^3 =  [#permalink]

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New post 13 Feb 2017, 02:16
3
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (01:15) correct 30% (01:37) wrong based on 225 sessions

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7^3 + 21^3 =  [#permalink]

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New post 13 Feb 2017, 02:56
2
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
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Re: 7^3 + 21^3 =  [#permalink]

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New post 13 Feb 2017, 05:20
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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. \(7^4*3^3\)



21^3 = (7*3)^3 = 7^3*3^3

7^3 + 21^3 taking 7^3 common
7^3(1+3^3) = 7^3(28)
28= 7*4 = 7*2^2

thus 7^3(7*2^2)
= 7^4*2^2

Ans A
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Re: 7^3 + 21^3 =  [#permalink]

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New post 13 Feb 2017, 08:26
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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. \(7^4*3^3\)


\(7^3 + 21^3\)

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

= \(7^3 (1 +3^3 )\)

= \(7^3 *28\)

= \(7^3 *7*2^2\)

= \(7^4 *2^2\)

Hence, answer will be (A) \(7^4 *2^2\)
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Re: 7^3 + 21^3 =  [#permalink]

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New post 14 Feb 2017, 15:50
1
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. \(7^4*3^3\)


We can simplify the given equation:

7^3 + 21^3

7^3 + (7x3)^3

7^3 + 7^3 x 3^3

7^3(1 + 3^3)

7^3(1 + 27)

7^3(28)

7^3 x 7^1 x 2^2

7^4 x 2^2

Answer: A
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Re: 7^3 + 21^3 =  [#permalink]

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New post 15 Feb 2017, 08:06
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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 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
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Re: 7^3 + 21^3 =  [#permalink]

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Re: 7^3 + 21^3 =   [#permalink] 22 Oct 2018, 05:29
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