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Ncert solutions
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Mathematics
Chapters in NCERT Solutions - Mathematics, Class 6
Exercises in Playing With Numbers
Question 4
Q4) Using divisibility tests, determine which of the following numbers are divisible by 11:
(a) 5445 (b) 10824 (c) 7138965 (d) 70169308 (e) 10000001
(f) 901153
Solution
Transcript
SOLUTION: divisibility by 11: if the difference between the sum of the digits at odd places and the sum of digits on even places of the number is either 0 or 11 it is divisible by 11
i) 5445
the sum of the odd places 5+4=9
the sum of the even places 4+5=9
9-9=0
since the difference between the sum of the odd places and the sum of even places is 0
it is divisible by 11.
ii) 10824
the sum of the odd places 1+8+4=13
the sum of the even places 0+2=2
13-2=11
since the difference between the sum of the odd places and the sum of even places is 11
it is divisible by 11.
iii) 7138965
the sum of the odd places 7+3+9+5=24
the sum of the even places 1+8+6=15
24-15=9
since the difference between the sum of the odd places and the sum of even places is 19
it is not divisible by 11.
iv) 70169308
the sum of the odd places 7+1+9+0=17
the sum of the even places 0+6+3+8=17
17-17=0
since the difference between the sum of the odd places and the sum of even places is 0
it is divisible by 11.
v) 10000001
the sum of the odd places 1+0+0+0=1
the sum of the even places 0+0+0+1=1
1-1=0
since the difference between the sum of the odd places and the sum of even places is 0
it is divisible by 11.
vi) 901153
the sum of the odd places 9+1+5=15
the sum of the even places 0+1+3=4
15-4=11
since the difference between the sum of the odd places and the sum of even places is 11
it is divisible by 11.