Latest CSC Aptitude Question SOLUTION: 1.5^20+5^7/7=? Reminderis………… 2. 12^82/72=? Remonder………… 3.11^99/18=? Reminder……… give its short cut

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(#M40038402) CSC Category question Keep an EYE

1.5^20+5^7/7=? Reminderis…………

2. 12^82/72=? Remonder…………
3.11^99/18=? Reminder………
give its short cut

Asked In CSC Anshu sharma (9 years ago)

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Saraswathy  (9 years ago)

1) 5^20+5^7/7
5^20 mod 7 + 5^7 mod 7
Since 5 nd 7 are co-primes, we can use Euler's theorem
E(7) = 6
So 5^E(7) = 1
5^20 mod 7 => (5^6)^3 * 5^2 mod 7
1 * 25 mod 7 = 4
Similarly 5^7 mod 7 => 5^6 * 5 mod 7
1 * 5 mod 7 = 5
Now 4 + 5 mod 7
9 mod 7 = 2
Ans : 2

2) 12^82 mod 72
(12^2)^41 mod 72
144^41 mod 72
(72*2 + 0)^41 mod 72
0^41 mod 72 = 0
Ans : 0

3) 11^99 mod 18
(18 - 7)^99 mod 18
(-7)^99 mod 18
E(18) = 6
(-7^6)^16 * (-7)^3 mod 18
1 * (-343) mod 18
-1 mod 18
(-1+18) mod 18 = 17
Ans : 17

Is this solution Helpfull? Yes (3) | No (9)  

virendra tiwari  (9 years ago)

5^20+5^7
5,25,125,625,3125,15625,78125,390625,1953125,9765625,,,,here last 3 digit in same sequence 625 and 125,even ana odd position soooo
5^20,, 20 even so last digit 625 and 7 odd mean 125
125+625=7507=rem 1... may be not sure

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