Latest TCS Aptitude Question SOLUTION: WHAT WILL BE THE REMANDER IF (34^31)^301 IS DIVIDED BY 9?

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(#M40025599) TCS Numerical Ability question NUMBER SYSTEM Keep an EYE

WHAT WILL BE THE REMANDER IF (34^31)^301 IS DIVIDED BY 9?

Asked In TCS keerthika manoharan (10 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

tejaswi boni  (10 years ago)

units digit of 31^301 is 1.
hence when 34^1/9 remainder is 7.

Is this solution Helpfull? Yes (39) | No (17)  

mehak jindal  (10 years ago)

34^31^301/9
(34*34*34)^8729/9
39304)^8729/9
=(9*4367+1)/9
1^8729/9
ans 1

Is this solution Helpfull? Yes (18) | No (13)  

roja  (10 years ago)

first of all we have 2 see the cycle of 34....
34*34=6
34*34*34=4
34*34*34*34=6
therefore cycle of 34 is 2..
301/2 remainder is 1.....
31/2 remainder is 1....
hence 34^1/9 has remainder 7

Is this solution Helpfull? Yes (8) | No (3)  

smr  (10 years ago)

34^6k divide by 9 gives 1
31^301 is 6k+1 type no.
so 34^6k+1= 34^6k * 34^1
hence 34^1 by 9 gives remainder 7
ans= 7

Is this solution Helpfull? Yes (2) | No (2)  

cvraj  (8 years ago)

31^301 =1 bcz unit digit is 1
therefore 34^1is 34
34%9=7

Is this solution Helpfull? Yes (2) | No   

Mrittika Bhaumik  (8 years ago)

First we need to get the remainder of 34/9 which is 7. Now if we divide 7's power series by 9 we get these remainders:-
7^1/9=7,7^2/9=4,7^3/9=1,7^4/9=7 and so on repeats this pattern of remainder of 7,4,1. so using this logic we get 7^31/9=7. so now we get 34^31/9=7 and similarly 7^301/9=7. So, we get the result as 7.

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smr  (10 years ago)

34/9 gives remainder of 7 or -2
thus 34^2 gives remainder of 4(-2*-2)
34^3 gives remainder of (-2*-2*-2)=-8 or 1
and, 34^31=34^(3k+1), so now we have to find remainder of (34)^301/9
since 34^301=34^(3k+1), so we r left with 34/9, as 34^3k gives 1 as remainder.

so finaly remainder is 34 mod 9= 7

Is this solution Helpfull? Yes (1) | No   

Pavithra Rajasekaran  (9 years ago)

34 mod 9 = 7

Is this solution Helpfull? Yes (1) | No   

bharani kumar  (10 years ago)

no of triangle=(87-1)/2=43
no of rectangle=43/2=21

Is this solution Helpfull? Yes | No (22)  

Guru Pranav  (10 years ago)

remainder will be 7. :)

Is this solution Helpfull? Yes | No (2)  

SumithraRengaraj  (9 years ago)

(32^1)/9=7 asw

Is this solution Helpfull? Yes | No (1)  

Rajanikanta Pradhan  (8 years ago)

(17*2)^31^301
=(17*2)^9331/9
=17^9331/9*2^9331/9
=-1*(2^3)^3110 *2/9
= -1*1*2/9
= rem -2 so 9-2 =7 rem

Is this solution Helpfull? Yes | No (1)  

happy das  (8 years ago)

first note that 34=3x9+7 so the remainder will the same as for 7^31^301.
When we look at the 7 table (modulo 9) we see that we have
7^1->7
7^2->4
7^3->1
and so on.
So the question is now related to 31^301 and how much 3 is in it.
And following the same idea, 31=10x3+1, we see that the remainder of the division of 31^301 by 3 is 1. So we are left with 7^1.
the answer is 7.

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Shahrukh  (8 years ago)

It will be 7

--->---->Rem [34^31^301 / 9] = Rem [7^31^301 /9]

Now, we need to observe the pattern
7^1 when divided by 9, leaves a remainder of 7
7^2 when divided by 9, leaves a remainder of 4
7^3 when divided by 9, leaves a remainder of 1
And then the same cycle of 7, 4, and 1 will continue.
If a number is of the format of 7^(3k+1), it will leave a remainder of 7
If a number is of the format of 7^(3k+2), it will leave a remainder of 4
If a number is of the format of 7^(3k), it will leave a remainder of 1

The number given to us is 7^31^301
Let us find out Rem[Power / Cyclicity] t0 find out if it 7^(3k+1) or 7^(3k+2). We can just look at it and say that it is not 7^3k
Rem [31^301/3] = Rem [1^301/3] = 1
=> The number is of the format 7^(3k + 1)
=> Rem [7^31^301 /9] = 7

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