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 7 of 7.
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.
Nitin Sharma said:
10 years ago
Dividend = Divisor*Quot+Remainder.
Here, Dividend is '67^67 + 67' and divisor is 68.
i.e 67^67 + 67 = 68*Quot+Remainder.....(1).
Now, we know that (x^n + 1) will be divisible by (x + 1) only when n is odd. --> Theory.
We express Dividend as follows: (67^67+1)*1+66.....(2).
i.e. 67^67+67 = 68*Quot+Remainder.....(from 1).
Comparing the above.
Here, Dividend is '67^67 + 67' and divisor is 68.
i.e 67^67 + 67 = 68*Quot+Remainder.....(1).
Now, we know that (x^n + 1) will be divisible by (x + 1) only when n is odd. --> Theory.
We express Dividend as follows: (67^67+1)*1+66.....(2).
i.e. 67^67+67 = 68*Quot+Remainder.....(from 1).
Comparing the above.
Sanjay said:
10 years ago
Simple method of this problem is 67+67 = 134-68 = 66.
Reshma said:
9 years ago
What would be the solution when n is even?
Meghana said:
9 years ago
Why do we subtract 2 the remainder from 68, can anyone explain this?
Nivas said:
9 years ago
The formula is a^n + b^n is divisible by a + b if n is odd.
Ambika said:
9 years ago
Why do we subtract 2 from 68?
Sharanya said:
9 years ago
Give more clarity about this question.
Shru said:
9 years ago
It's very easy, Thank you @Mahi.
Narendra said:
1 decade ago
Please suggest me another method.
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