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08 Feb 2021, 08:00
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
70% (01:45) correct
30%
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wrong
based on 165
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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
A. 1
B. 2
C. 3
D. 4
E. 5
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
A. 3
B. 4
C. 1
D. 5
E. 2
hykhan
Current Student
Joined: 18 Dec 2020
Last visit: 04 Aug 2022
Posts: 87
Given Kudos: 28
Location: Canada
Concentration: Healthcare, Entrepreneurship
Schools: Judge '23 (M$) INSEAD Aug 22 intake (A)
GMAT 1: 700 Q47 V39
GMAT 2: 720 Q48 V41
GPA: 2.8
WE:Project Management (Pharmaceuticals and Biotech)
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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
Posted from my mobile device
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
Posted from my mobile device
08 Feb 2021, 08:43
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Bookmarks
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
Posted from my mobile device
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
Posted from my mobile device
