Latest TCS Aptitude Question SOLUTION: what is the remainder when 50! Divided by 47^2.

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(#M40012360) TCS Logical Reasoning question Keep an EYE

what is the remainder when 50! Divided by 47^2.

Asked In TCS div (11 years ago)

Unsolved Read Solution (16)

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Read Solution (16) :

tanu goel  (11 years ago)

first understand dis
(6*10*55)/9
remainder of this is 6. there r two ways to calculate this
1--- 6*10*55 ie 3300 mod 9 = 6
2--- 6 mod 9 =6
10 mod 9 =1
55 mod 9=1
thn multiply all the rem n u get the ans ie 6

in case of 47^2
50*49*48*47*46! / 47^2
47 will b cancel out
50*49*48*46 ! / 47
nw find out remainder individually
50 % 47 =3
49 % 47 =2
48 % 47=1
and acc to wilson theorem
if p is a prime no thn (p-1)! mod p =-1
here 47 is a prime no so
46!% 47 = -1 or 46
so multiply all the rem
3 * 2*1* 46 mod 47 = 276 mod 47 = 41
nw multiply 41 with 47 so we get
41*47= 1927...ans

Is this solution Helpfull? Yes (41) | No (5)  

Shalu Jain  (11 years ago)

According to wilson's theorem
For a prime number p,
rem[(p-1)!/p]=p-1

50!/47^2
=(50*49*48*47*46!)/47^2
=(50*49*48*46!)/47
overall rem=(3*2*1*46)
=276
276 is greater than 47
so
rem= 276 mod 47
=41 (Ans)

Is this solution Helpfull? Yes (12) | No (2)  

sandeep pandey  (10 years ago)

(1+2+3...+50-47)/47 the rem is answer 1+2+3...+50 is a.p. series easy to find the sum.

Is this solution Helpfull? Yes (2) | No   

chiru  (11 years ago)

can any one xplain dis...

Is this solution Helpfull? Yes (1) | No (2)  

Kiran Pradhan  (11 years ago)

ans=17.......

Is this solution Helpfull? Yes (1) | No (7)  

prachitrivedi  (11 years ago)

pls explain

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Saurabh Awasthi  (11 years ago)

ans is 4.....

Is this solution Helpfull? Yes (1) | No (4)  

goldy  (11 years ago)

ans is 43......

Is this solution Helpfull? Yes (1) | No (4)  

Pratik sharma  (9 years ago)

Answer should be 6
because
50*49*48*47!/(47*47) which cancel one 47
thus left with
(50*49*48/47)..now by remainder theorem it ll be 3*2*1=6

Is this solution Helpfull? Yes (1) | No (2)  

niki  (11 years ago)

i think ans is 3.

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shivi vaish  (11 years ago)

ans :6.....

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Ravi Bhole  (11 years ago)

50!= 2^47 x3^21x5^11x7^8x11^4x13^3x17^2x19^2x23^2x29x31x37x41x43x47 /47^2
=2^47 x3^21x5^11x7^8x11^4x13^3x17^2x19^2x23^2x29x31x37x41x43x47^-1

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R LAKSHMAN  (10 years ago)

the answer is 1927

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mounika  (10 years ago)

why u'r again multiply with 47 tanu goel?????
please tell me reason.........

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Arpita Kapoor  (9 years ago)

one 47 will get cancelled

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apurva parashar  (9 years ago)

50*49*48*47/(47*47)= 47 cancels 47.=(50*49*48)/47.
divide individually.= 3*2*1=6 answer

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