Question

$5^{17}+5^{18}+5^{19}+5^{20}$ is divisible by

• A. $7$
• B. $9$
• C. $11$
• D. $13$

Answer 1

Answer: (A)

$7$

we can also write

$=>5^{(}18+19+20)$

$=>5^{(}74)$

$=119018554687500$

check condition for $9$

We see that,this number is even ending to zero and since the sum of its digit is divisible by $3$ $(1+1+9+0+1+8+5+5+4+6+8+7+5+0+0)=60$ which is divisible by $3$

$\frac{119018554687500}{3}=39672851562500$

now, we see that $3+9+6+7+2+8+5+1+5+6+2+5+0+0=59$ which is not divisible by $3$

hence,original number is nit divisible by $9$

check condition for $11$

$1-1+9-0+1-8+5-5+4-6+8-7+5-0+0=6$

which is not divisible by $11$

check condition for $7$

you must ake last digit and double it and subtract this number from the rest of remaining digit

number is $119018554687500$

last digit is $0$

and subtract from remaning digit

$11901855468750-0=11901855468750$

which is not divisible by $7$

check condition for $13$

pair of three digit from the right side of digit and arrange with alternating sign of positive negative

i.e.,

$500-687+554-018+119=468=\frac{468}{13}=36$

therfore,the number is divisible by $13$