Latest CAT Aptitude Question SOLUTION: what is the reminder when 7^7oo is divided by 100? options: (a)1 (b)41 (c)41 (d)21

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(#M40011729) CAT question Keep an EYE

what is the reminder when 7^7oo is divided by 100?

options:
(a)1 (b)41 (c)41 (d)21

Asked In CAT dhivyabharathi (11 years ago)

Unsolved Read Solution (5)

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avantika gautam  (11 years ago)

1 is the answer...as u can check that 7^1=7,7^2=9(units plc),7^3=3(unit plc),7^4=1 and 7^5=again 7 at unit's plc... so variation is after 4powers...so divide the power by 4 n c what remaindr it gives...700/4=175 no remaindr...so it will end upto 4powers...so value of the 4th power is 1... n so when 100 will divide it it will give 1as its remainder...

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kck  (11 years ago)

answer : 1
explanation:
7^700 can be written as..(7^4)^175=(2400+1)^175
as we know ,if we expand this by binomial theorem we have each term except last is divisible by 100 ....hence remainder is last term i.e 1^175.
so answer is 1.

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BRIJESH KUMAR GUPTA  (11 years ago)

7^4=2401 and 7^700=(7^4)^175
so rem =1*1*...175 times=1

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PARAG KAMRA  (11 years ago)

7^700 mod 100
[(((7)^3)^233).(7)^1] mod 100
[((343)^233) .7] mod 100
(100*3+43)^233 .7 mod 100
(43)^243 .7 mod 100
now we take only (43)^243 .7mod (10*10)
so first (43)^243 .7 mod 10
(10*4+3)^243 .7 mod 10
3^243 .7 mod 10
27^81 .7 mod 10
(10*2+7)^81 .7 mod 10
7^81 mod 10
(7^2)^40.7.7 mod 10
(49)^40 .49 mod 10
(10*4+9)^40 .49 mod 10
(9)^40 .49 mod 10
(10-1)^40.49 mod 10
(-1)^40 .49 m0d 10
so it will be 1*49=49
so we 49 mod 10=9
so 9 will be remainder when 7^7oo is divided by 100

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

darshan tumballi  (11 years ago)

7^700=(7^4)^28...
7^4 %100=1
=>(7^4)^28 %100 =1^28 %100
=1;

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