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# An “Armstrong number” is an n-digit number that is equal to the sum of

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Senior Manager
Joined: 04 Sep 2017
Posts: 291
An “Armstrong number” is an n-digit number that is equal to the sum of  [#permalink]

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21 Sep 2019, 14:21
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Difficulty:

55% (hard)

Question Stats:

67% (02:42) correct 33% (02:48) wrong based on 48 sessions

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An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4 ?

A. 2
B. 3
C. 4
D. 5
E. 6

PS36302.01
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Joined: 29 Jun 2019
Posts: 408
Re: An “Armstrong number” is an n-digit number that is equal to the sum of  [#permalink]

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21 Sep 2019, 22:00
1⁴+6⁴+k⁴+4⁴=1604+10k
1+1296+k⁴+256=1604+10k
k⁴-10k=1604-1553=51
By replacing the options with k, 3 would be the answer.
3⁴-30=51
Option B

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Re: An “Armstrong number” is an n-digit number that is equal to the sum of  [#permalink]

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22 Sep 2019, 02:02
digit 16k4 ; 1^4+6^4+k^4+4^4
so test with each option value
at k=3 we get 1634 =1^4+6^4+3^4+4^4
IMO B

gmatt1476 wrote:
An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4 ?

A. 2
B. 3
C. 4
D. 5
E. 6

PS36302.01
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Joined: 14 Apr 2017
Posts: 66
Location: Hungary
GMAT 1: 760 Q50 V42
WE: Education (Education)
Re: An “Armstrong number” is an n-digit number that is equal to the sum of  [#permalink]

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22 Sep 2019, 05:15
1
gmatt1476 wrote:
An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4 ?

A. 2
B. 3
C. 4
D. 5
E. 6

PS36302.01

$$1^4+6^4+k^4+4^4=16k4$$

The units digits of $$1^4$$, $$6^4$$, and $$4^4$$ are 1, 6, and 6, respectively. Since 1+6+6=13, the units digit of $$k^4$$ must be 4-3=1.

The only answer choice whose 4th power has a unit digit of 1 is B.

Answer: B
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Re: An “Armstrong number” is an n-digit number that is equal to the sum of   [#permalink] 22 Sep 2019, 05:15
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# An “Armstrong number” is an n-digit number that is equal to the sum of

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