A number 'n' when divided by 4 leaves a remainder 3. Which of these could be the remainder when 'n' is divided by 8?
a) 4
b) 5
c) 1
*Q16 if you want to refer to the picture*
Answers
given : A number 'n' when divided by 4 leaves a remainder 3.
To Find : Which of these could be the remainder when 'n' is divided by 8?
a) 4
b) 5
c) 1
Solution:
A number 'n' when divided by 4 leaves a remainder 3.
=> n = 4k + 3
4k + 3 = 8p + r
r is the remainder
r = 4k + 3 - 8p
now k can be even or odd
Case 1 = k = 2m
r = 4(2m) + 3 - 8p
=> r = 8(m - p) + 3
=> r = 8q + 3
Hence 3 can be remainder
case 2 : k = 2m + 1
=> r = 4(2m+ 1 ) + 3 - 8p
=> r = 8(m - p) + 4 + 3
=> r = 8(m - p) + 7
=> r = 8q + 7
Hence 3 can be the remainder
so 3 or 7 can be the remainder
none of the given options are correct
Examples are 11 and 15
15 = 4 x 3 + 3 = 8 x 1 + 7
11 = 4 x 2 + 3 = 8 x 1 + 3
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Answer:
3 or 7
Step-by-step explanation:
the remainder could be 3 or 7