Aptitude - Numbers - Discussion

Discussion Forum : Numbers - General Questions (Q.No. 30)
30.
What will be remainder when (6767 + 67) is divided by 68 ?
1
63
66
67
Answer: Option
Explanation:

(xn + 1) will be divisible by (x + 1) only when n is odd.

(6767 + 1) will be divisible by (67 + 1)

(6767 + 1) + 66, when divided by 68 will give 66 as remainder.

Discussion:
70 comments Page 6 of 7.

Vipin raj said:   7 years ago
X^n + 1 is divisible by x+1 always whatever the value of n.
X^n -1 is divisible by x+1 and x +1 and x -1.

That same the given value 67^67. +1, +66 extra port of this no will be remainder.
(1)

Aakash said:   7 years ago
Please anyone explain clearly. I can't understand.

Mamatha said:   6 years ago
@Sivaram.

It was very helpful. Thanks.

Wesly said:   6 years ago
Thanks for the clear explanation, @Padmaja.

Random retard said:   6 years ago
Thanks to all the good souls who took time to explain the answer.

Vasanthi said:   6 years ago
I didn't understand the concept. Please explain it for me.
(2)

Kamal hachan said:   5 years ago
(67^67+67)%68 where % is mod operator. it gives remainder.
= 67^67%68+67%68
=(68-1)^67%68 +(68-1)%68
=(-1)^67+(-1)
= -1-1
=-2 (Since remainder can't be negative )
=68-2
= 66
believe me this is best trick for remainder
If any doubt please email me.
(8)

Bhaskar said:   5 years ago
By using binomial theorem.
((68-1)^67+67)/68.

All term which includes 68 will be divided by 68.
Then((-1)^67+67)/68 will be left,
It becomes 66/68.
Hence remainder is 66.
(6)

Suma said:   5 years ago
I didn't understand, Anyone Help me out.
(4)

Barath said:   4 years ago
Using unit digit method : 67 power 67 is 343 and we will add 343 +67.

410 and it is divided by 68 then the remainder will be 2.
(4)


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