Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 30)
30.
What will be remainder when (6767 + 67) is divided by 68 ?
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 3 of 7.
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.
((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)
Pushpendra Shukla said:
4 years ago
(x^n - a^n) is divisible by (x - a) for all values of n.
(x^n - a*n) is divisible by (x + a) for even values of n.
(x^n + a^n) is divisible by (x + a) for odd values of n.
(x^n - a*n) is divisible by (x + a) for even values of n.
(x^n + a^n) is divisible by (x + a) for odd values of n.
(5)
Kalai said:
1 decade ago
We take the odd number 67 and divide it by even 68, the remainder is 1 less than the odd number.
So, the remainder when (67^67 + 67) is divided by 68 will be 67 -1 = 66.
So, the remainder when (67^67 + 67) is divided by 68 will be 67 -1 = 66.
(1)
Anuj said:
1 decade ago
(67^67+67)/68 = 67^67/68+67/68.
If we 67/68 = -1 remainder.
So ((-1)^67-1)/68 = (-1-1)/68.
i.e.(-2)/68 = remainder can't negative then 68-2 = 66 answer.
If we 67/68 = -1 remainder.
So ((-1)^67-1)/68 = (-1-1)/68.
i.e.(-2)/68 = remainder can't negative then 68-2 = 66 answer.
Ummar said:
3 years ago
@All.
Here is the solution;
67 * 2 - 68 = remainder = 66.
Valid for any type of formation like the given one.
n*2-(n+1) = remainder.
Here is the solution;
67 * 2 - 68 = remainder = 66.
Valid for any type of formation like the given one.
n*2-(n+1) = remainder.
(34)
Vijay said:
1 decade ago
Check numbers from 3, 4, 5, ... , in the above given format. We will get remainder 1 less than the number, so for 67^67+67 = 66.
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.
410 and it is divided by 68 then the remainder will be 2.
(4)
Rishabh said:
1 decade ago
67^67 = (68^67-1^67).
So (68^67)+67-1^67.
= (68^67)+66.
= (68^67) is completely divisible by 68. So remainder is 66.
So (68^67)+67-1^67.
= (68^67)+66.
= (68^67) is completely divisible by 68. So remainder is 66.
Deepak said:
1 decade ago
Find out unity digit of 67^67....i e unit digit is 3
n 3+67=70
and when divide by 68 remainder 2...ie 68-2=66
n 3+67=70
and when divide by 68 remainder 2...ie 68-2=66
Abhishek said:
10 years ago
67/68 remainder -1 then (-1) to the power 67 is -1.
+67/68 remainder is 67.
So answer 67-1=66.
+67/68 remainder is 67.
So answer 67-1=66.
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