official quant thread for cat08

[MaskedMenace]

Seems Like Thread is not very active tode....think its Off today..neways..ques frm my side

(6^83 + 8^ 83) / 49 Find remainder ?

[shivam_01]

Originally Posted by MaskedMenace

Seems Like Thread is not very active tode....think its Off today..neways..ques frm my side

(6^83 + 8^ 83) / 49 Find remainder ?

@Masked menance
The remainder is 35 only

[vivek417]

Originally Posted by shivam_01

@Masked menance
The remainder is 14 only

I am getting 35 as remainder...
My solution..

6^83+8^83 = (7-1)^83 + (7+1)^83

Hence all the terms would be divisible by 49 except last 2

So we r left with 83C82 * 7 - 1 + 83C82 * 7 + 1
= 83*7*2 = 34*7*2 = 35

Thanks
Vivek

[aishmaadi]

Originally Posted by shivam_01

@Masked menance
The remainder is 14 only

how is it 14 man ..
plzz explain ..

[aishmaadi]

Originally Posted by vivek417

I am getting 35 as remainder...
My solution..

6^83+8^83 = (7-1)^83 + (7+1)^83

Hence all the terms would be divisible by 49 except last 2

So we r left with 83C82 * 7 - 1 + 83C82 * 7 + 1
= 83*7*2 = 34*7*2 = 35

Thanks
Vivek

seems corrrect ..
nice

[shivam_01]

Originally Posted by aishmaadi

how is it 14 man ..
plzz explain ..

see
6^83+8^83 in this case
E.N of 49 is 42 so we can write

6^83+8^83 as 6^-1 + 8^-1 where remaindder will be 14 only

lets c what is the take of the masked menance

[masoom]

Originally Posted by shivam_01

see
6^83+8^83 in this case
E.N of 49 is 42 so we can write

6^83+8^83 as 6^-1 + 8^-1 where remaindder will be 14 only

lets c what is the take of the masked menance

i also did by viveks method..

make it (7-1)^83+ (7+1)^83...

so ondividind by 49 the terms remaining are..

83C82 *7 -1 + 83C82 *7 +1..

2*83*7

means 2*83*7 (mod) 49...

2*83(mod)7....

which comes to be 5...

since we cancelled 7...

so effective remainder is 5*7=35...

[shivam_01]

Originally Posted by shivam_01

see
6^83+8^83 in this case
E.N of 49 is 42 so we can write

6^83+8^83 as 6^-1 + 8^-1 where remaindder will be 14 only

lets c what is the take of the masked menance

sorry ya got it the answer will be 35 only as i am getting the answer as -14 which
-14 mod 49 will generate remainder as 35

[masoom]

Originally Posted by shivam_01

see
6^83+8^83 in this case
E.N of 49 is 42 so we can write

6^83+8^83 as 6^-1 + 8^-1 where remaindder will be 14 only

lets c what is the take of the masked menance

dud 6^-1 is 1/6 and 8^-1 is 1/8...

adding we get 7/24...

how you are getting it as 14...

[vivek417]

Nice to see almost everyone online....it seems as if it is a normal weekday.....

Thanks
Vivek