Latest Elitmus Aptitude Question SOLUTION: Remainder when 30^72^87 divided by 11

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Remainder when 30^72^87 divided by 11

Asked In Elitmus shuvaranjan dash (10 years ago)

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RAKESH  (10 years ago)

if its 30^(72^87)/11

72^87 gives unit digit 8 so it can be written as (10k + 8)

30^(10k+8)/11
=> 30^10k * 30^8 / 11
=> (-3)^10k * (-3)^8 / 11
=> (3^5)^2k * (3)^5* 3^3 / 11
=> (11*22+1)^2k * (11*22+1)^5 * 27 / 11
=> 1^2k * 1^5 *27 /11
=> 27/11
=> rem = 5

Is this solution Helpfull? Yes (33) | No (8)  

RAKESH  (10 years ago)

if its (30^72)^87/11

(30^72)^87/11
=> 30^6264/11
=> (11*3-3)^6264/11
=> (-3)^6264/11
=> ((-3)^2)^3132/11
=> 9^3132/11
=> (11-2)^3132/11
=> 2^3132/11
=> (2^5)^626* 2^2 /11
=> (33-1)^626 * 4 /11
=> 4/11
=> rem = 4

Is this solution Helpfull? Yes (25) | No (11)  

shuvaranjan dash  (10 years ago)

dear rakeshbhaya,the answer given in arun sharma for this problem is 5

Is this solution Helpfull? Yes (10) | No (1)  

anirduh  (10 years ago)

please notify me where i am wrong according to me ans is 7
here is my calculations
according to remainder theorem
30*72*87/11 --R->(-3)(6)(-1)/11 =(18)/11-R-->7ANS

Is this solution Helpfull? Yes (5) | No (6)  

Rahul Das  (10 years ago)

i thimk it will be 7

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AVIJIT  (10 years ago)

: Fermat little theorem says, ap−1p remainder is 1.
ie., 30^10 or 8^10when divided by 11 remainder is 1.
The unit digit of 72^87 is 8 (using cyclicity of unit digits) Click here
So 72^87 = 10K + 8
30^(10K+8) / 11=(30^10)K.30^8/11=1k.30811
8^8/11=2^24/11=(2^5)4.2^4/11=16^11=5

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CHAITANYA  (10 years ago)

11)30(2
22
---------
08............REMAINDER
WHAT EVER THE VALUE OF 30^X TAKE ONE 30 FROM 30^X FOR DIVDING BY 11

Is this solution Helpfull? Yes (1) | No   

Mani kandan  (10 years ago)

HCF ( 30 , 11 ) is 3.
where phi(11)=(1-1/11)*11=10

so, 7287 = 10k + 8
=> 3072^87 = 30(10k + 8) = 308mod11 = (-3)8mod11 = 33mod11 [ 35 = 1mod11]
= 27mod11 = 5

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SUDHIR SHARMA  (10 years ago)

5 will be the correct Answer.
Because when u calculate unit digit of 72^87 it will give 8 as unit digit.
Therefore when 30^8 is divided by 11 , using Remainder Theorem we will get
5 as remainder.

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rochit ranjan  (9 years ago)

@rakesh why answer is not equal to 4 ? could you please explain ?

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Ehtesham  (9 years ago)

(30^72)^87 this can be written as : 30^6264

and 30^6264 can be written as : (30^2)^3132=900^3132

900^3132/11= (11* 80+ 10)^3132/11
=10^3132/11
=(11-1)^3132/11
=1 (since ,power is positive )

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