Latest TCS Aptitude Question SOLUTION: 76^77 /7 remainder is ?

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(#M40034037) TCS Numerical Ability question Need Solution Keep an EYE

76^77 /7
remainder is ?

Asked In TCS Ghanshyam Gulati (10 years ago)

Solved sandy Read Solution (15)

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Read Solution (15) :

sandy  (10 years ago)

@Ghanshyam Gulati
ANS IS:6
when u see problems like this(that is consecutive numbers(76 POWER 77))
or
FOR EXAMPLE
((32)^(33)^(34))/33
WRITE THEM LIKE THIS: (32*33*34)/33
THEN JUST DIVIDE INDIVIDUALLY =>(-1*1*+1)/33
SO ANSWER WILL BE -1/33 I.E., 33-1=32(REMAINDER)
COMING TO THE QUESTION (76^77)/7 JUST WRITE IT LIKE THIS (76*77)/7
THEN (-1*1)/7=>-1/7=>7-1=6(REMAINDER)

Is this solution Helpfull? Yes (23) | No (1)  

soumi sen  (10 years ago)

as, 4^3/3=64/3 remainder=1 and also 4/3=1
and 5^3/3 remainder=2 and also 5/3=2
so it does not matter on the power value
so the answer will be 76/7 remainder=6

Is this solution Helpfull? Yes (5) | No   

Saraswathy  (10 years ago)

6 will be the remainder

(ax-1)^n/a will gives the remainder "1" for all even values of 'n' and "(a-1)" for all the odd values of 'n'

here 76^77/7 ==> (7*11-1)^77/7 [a=7, x=11,n=77]

here power "n" is odd

so the remainder is (a-1) ie (7-1) which is "6"

Ans : 6

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

Saumya Agarwal  (9 years ago)

we can write the question as(70+6)^77/7
thus everytime we'll get 6 as remainder,((6)^77/7)
now,we can write it ((7-1)^77/7),
thus now remainder would be((-1)^77/7)
77 is odd thus (-1)/7=6
ans:6

Is this solution Helpfull? Yes (2) | No   

Dharmendra Shukla  (9 years ago)

(77-1)^77/7=(-1)^77
=-1 but the remainder can not be negative
so rem=-1+divisor=-1+7=6

Is this solution Helpfull? Yes (2) | No   

sanket patel  (9 years ago)

76^77/7=(77 times 76)/7
=76*76*76*76*....76(77times)/7
now divide each 76 by 7
=76/7 * 76/7 * 76/7 * ....76/7(77 times)
now you will get 6 as reminder
=6/7 * 6/7 * 6/7 *...6/7(77times)
now ,multiply each term's nominator and divide by 7
=36/7 * 36/7 * 36/7 *....36/7(38times) *6/7
now you will get reminder as 1 for each term
=1/7 * 1/7 *1/7....1/7(38times) * 6/7
now multiply each nominator again
=1(38 times)/7 * 6/7
=1/7 * 6/7
now again multiply nominator
=6/7
and you will get 6 as final reminder.

Is this solution Helpfull? Yes (1) | No   

vaishali gupta   (9 years ago)

(7*11-1)^77 / 7=(-1)77/7
7-1=6
so ans is 6

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Sourav ganguly  (9 years ago)

76%7=6
whatever may be the power of 6. unit digit will be 6
so remainder is 6

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ARCHIE GUPTA  (9 years ago)

7*11-1/7
(-1)^77/7=-1
7-1=6

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aditya jain  (9 years ago)

76^77/7
(-1)^77/7
-1/7
REM -1 OR 6

Is this solution Helpfull? Yes (1) | No   

SANAPALA SIVARAMAKRISHNA  (10 years ago)

last 2 digits 0f 76^77 is 96.after dividing 96 by 7 remainder is 5

Is this solution Helpfull? Yes | No (7)  

sanket patel  (9 years ago)

76^77/7=(77 times 76)/7
=76*76*76*76*....76(77times)/7
now divide each 76 by 7
=76/7 * 76/7 * 76/7 * ....76/7(77 times)
now you will get 6 as reminder

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rahul  (9 years ago)

ans is 6 as expression is of the form a^n/a+1
76^77/7 = 6^77/7

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priteesudha tayade  (9 years ago)

zero..as77/7=11 i,e zero remainder

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arockia pushparaj  (9 years ago)

ans:6
the given data 76^77/17 formula:a^n/(a+1) if n is odd=a if n is even=1 so the sum last unit digit 6^77 power is odd.the ans is 6.

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