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# 7^3 + 21^3 =

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13 Feb 2017, 02:16
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Difficulty:

25% (medium)

Question Stats:

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

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$$7^3 + 21^3 =$$

A. $$7^4*2^2$$

B. $$7^3*2^4$$

C. $$7^3*3^3$$

D. $$7^3*3^4$$

E. $$7^4*3^3$$

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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

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Re: 7^3 + 21^3 =  [#permalink]

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13 Feb 2017, 05:20
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. $$7^4*3^3$$

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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13 Feb 2017, 08:26
4
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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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

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Re: 7^3 + 21^3 =  [#permalink]

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15 Feb 2017, 08:06
1
Top Contributor
2
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

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

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Re: 7^3 + 21^3 =  [#permalink]

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