Latest TCS Aptitude Question SOLUTION: 6^17+17^6/7 what will be the remainder

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(#M40019958) TCS Logical Reasoning question Keep an EYE

6^17+17^6/7 what will be the remainder

Asked In TCS (11 years ago)

Unsolved Read Solution (15)

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Read Solution (15) :

Shiva  (11 years ago)

6^17+17^6/7=((7-1)^17+(7*2+3)^6)/7=-1+((3)^6)/7=-1+((3^3)^2)/7=-1+((28-1)^2)/7
so remainder vll be -1+(-1)^2=-1+1=0

Is this solution Helpfull? Yes (21) | No (6)  

saurabh keshari  (11 years ago)

answer is 0
solution:
(6^17+17^6)/7
(-1)^17 + (3)^6
-1 + (3^2)^3
-1 + 2^3
-1 + 1 => 0

Is this solution Helpfull? Yes (3) | No   

Mukesh kumar  (11 years ago)

since a^n/(a+1)=a when n is odd
and (ax + 1)^n /a =1 for any value of n
so 6^17/7= 6 and 3^6/7=729/7=(728+1)/7=(7*104+1)/7=1
i.e 6+1/7=7/7=0
hence remainder is 0

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

Priyanka Ganguly  (11 years ago)

6-3=3
6^17 will make a remainder of 6
and 17^6/7 will make remainder of -3
so total remainder is 3

Is this solution Helpfull? Yes (2) | No (4)  

ashiwani kumar singh  (11 years ago)

r(6^17)=6;
r(7^6)=3;
6+3=9/7;
r(9/7)=2;

Is this solution Helpfull? Yes (1) | No (1)  

Shikha Sinha  (11 years ago)

if the ques is (6^17+17^6)/7, then we can write ((7-1)^17)/7+(14+3)^6/7
=-1^17/7+(3^2)^3/7
=(-1/7)+(7+2)^3/7
=-1/7+8/7
so rem is -1+1=0 ans.

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vaasa nagesh  (11 years ago)

617 = (7−1)17 =
17C0.717−17C1.716.11.....+17C16.71.116−17C17.117

If we divide this expansion except the last term each term gives a remainder 0. Last term gives a remainder of - 1.

Now From Fermat little theorem, [ap−1p]Rem=1
So [1767]Rem=1

Adding these two remainders we get the final remainder = 0

Is this solution Helpfull? Yes (1) | No   

ZP  (9 years ago)

answer is zero
solution :
[ (7-1)^17 ] / 7 + [ ( 14+3) ^ 6 ] / 7
-1 ^ 17 + (3^6) / 7
-1 + [3^(2*3)] / 7
-1 + (9^3) / 7
-1 + ( 2^3) / 7
-1 + 8/7 = -1 + 1 = 0 :)

Is this solution Helpfull? Yes (1) | No   

ajay jain  (11 years ago)

ans is 2
6^7/7 reminder is -1
17^6/7 reminder is 3
then 3-1 = 2

Is this solution Helpfull? Yes | No (7)  

Narendra  (11 years ago)

plz any one tell clear explantion

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Amit kumar jha  (11 years ago)

((6^2)^8*6)/7 +(17^6)/7
((36)^8*6)/7+(3)^6
(1)^8*6+729
6+729
735

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Tejaswi  (11 years ago)

dear admin......plz explain the solution clearly.......

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mugala nagaraju  (11 years ago)

ans is: 6+1 =7
logic: according to "FERMATS RULE" we can do
ie...if gcd(a,p)=1 then a^(p-1)=1mod(p)
here p is 7 and we have to calculate indivisual

Is this solution Helpfull? Yes | No (1)  

pratyush gupta  (10 years ago)

0 7

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GOWRABATHUNI RAJESH  (10 years ago)

0 is the answer because

6^7mod7 can be written (7-1)^7 mod 7=-1
17^6mod7 can be written (7*2+3)^6mod7=3^6mod7=729 mod7=1

-1+1=0

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