Question

A positive integer n when divided by 9, gives 7 as remainder . What will be the remainder when (3n-1) is divided by 9 ?

(a) 1 (b) 2 (c) 3 (d) 4​

Answer 1

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$\large\mathcal\red{solution}$

when n is divided by 9 it gives a remainder of 7...

now ...n=9m+7

where m is a positive integer...

for m=1

n=9(1)+7=16

for m=2

n=9(2)+7=25

for m=3

n=9(3)+7=34

so..on...

now ....for n=16

3n-1=47

therefore remainder when divided by 9 is=2

as 9×5=45

now.... for n=25

3n-1=74

therefore remainder when divided by 9 is=2

as 9×8=72

now....for n=34

3n-1=101

therefore remainder when divided by 9 is=2

as 9×11=99

therefore the remainder will be 2 when (3n-1) is divided by 9

$\underline{\large\mathcal\red{hope\: this \: helps \:you......}}$