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When a positive integer x is divided by 6, remainder obtained is 3. Wh

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Bunuel
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When a positive integer x is divided by 6, remainder obtained is 3. Wh [#permalink] New post   08 Feb 2021, 08:00
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When a positive integer x is divided by 6, remainder obtained is 3. What is the remainder when \(x^4 + x^3 + x^2 + x + 1\) is divided by 6?

A. 1
B. 2
C. 3
D. 4
E. 5

Show Spoiler
When x is divided by 6, remainder obtained is 3. Find the remainder when \(x^4 + x^3 + x^2 + x + 1\) is divided by 6.

A. 3
B. 4
C. 1
D. 5
E. 2
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A
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hykhan
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Re: When a positive integer x is divided by 6, remainder obtained is 3. Wh [#permalink] New post   08 Feb 2021, 08:28
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X = 6Q + 3

X^4 = 1296Q + 81
X^3 = 216Q + 27
X^2 = 36Q + 9
X = 6Q + 3

81+27+9+3+1 = 121

121/6 = 20 and 1/6

Remainder = 1

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Re: When a positive integer x is divided by 6, remainder obtained is 3. Wh [#permalink] New post   08 Feb 2021, 08:43
Given: When a positive integer x is divided by 6, remainder obtained is 3.
Asked: What is the remainder when \(x^4 + x^3 + x^2 + x + 1\) is divided by 6?

x = 6k + 3
x^2 = 36k^2 + 36k + 9 = 6m + 3
x^3 = 36km + 18k + 18m + 9 = 6n +3
x^4 = 36m^2 + 36m + 9 = 6l +3

x^4 + x^3 + x^2 + x + 1 = (6k+3) + (6m+3) + (6n+3) + (6l+3) +1 = 6(k+m+n+l+2) +1

IMO A

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Re: When a positive integer x is divided by 6, remainder obtained is 3. Wh [#permalink] New post   08 Feb 2021, 08:45
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Bunuel both answer choices A & B are same. Please correct

Bunuel wrote:
When a positive integer x is divided by 6, remainder obtained is 3. What is the remainder when \(x^4 + x^3 + x^2 + x + 1\) is divided by 6?

A. 1
B. 1
C. 3
D. 4
E. 5

Show Spoiler
When x is divided by 6, remainder obtained is 3. Find the remainder when \(x^4 + x^3 + x^2 + x + 1\) is divided by 6.

A. 3
B. 4
C. 1
D. 5
E. 2


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Bunuel
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Re: When a positive integer x is divided by 6, remainder obtained is 3. Wh [#permalink] New post   08 Feb 2021, 08:54
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Kinshook wrote:
Bunuel both answer choices A & B are same. Please correct

Bunuel wrote:
When a positive integer x is divided by 6, remainder obtained is 3. What is the remainder when \(x^4 + x^3 + x^2 + x + 1\) is divided by 6?

A. 1
B. 1
C. 3
D. 4
E. 5

Show Spoiler
When x is divided by 6, remainder obtained is 3. Find the remainder when \(x^4 + x^3 + x^2 + x + 1\) is divided by 6.

A. 3
B. 4
C. 1
D. 5
E. 2


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Re: When a positive integer x is divided by 6, remainder obtained is 3. Wh [#permalink] New post   08 Feb 2021, 09:45
When a positive integer x is divided by 6, remainder obtained is 3. What is the remainder when x4+x3+x2+x+1x4+x3+x2+x+1 is divided by 6?

A. 1
B. 2
C. 3
D. 4
E. 5

Possible Solution, need your weigh-in on this Master Bunuel:
Can we assume the positive integer is 9? the remainder of 9 divided by 6 is 3.
so Assume the integer is 9.

(9^4+9^3+9^2+9+1)/6= 7381/6= 7380 with 1 remained, hence A.
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Re: When a positive integer x is divided by 6, remainder obtained is 3. Wh [#permalink]
08 Feb 2021, 09:45
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