Latest Elitmus Aptitude Question SOLUTION: a number divided by 13 leaves a remainder 1 and if the quotient,thus obtained is divided by 5,we get a remainder of 3.what will be the remainder if the number is divided by 65

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(#M40164540) ELITMUS Numerical Ability question Keep an EYE

a number divided by 13 leaves a remainder 1 and if the quotient,thus obtained is divided by 5,we get a remainder of 3.what will be the remainder if the number is divided by 65

Asked In Elitmus Sniper (7 years ago)

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GURKIRAT SINGH  (6 years ago)

let the no. be n
By remainder theorem :-
n=13q+1 -------------1 where q is quotient

also given

q=5t+3 -------------2 where t is quotient when q is divided by 5
put the value of eq 2 in eq 1 we get

n=65t + 40
Therefore 40 is the remainder

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gaurav kumar  (6 years ago)

If you don't know any concept regarding a problem,try hit and trial method by taking examples.As we can see that when the quotient is divided by 5 we get remainder as 3,so the quotient can be 8,13 etc.put quotient as 8 and we already know remainder was 1 when the number was divided by 13,hence the number comes out to be 13*8+1=105.Hence one such number which satisfies all the criteria given above is 105.Now upon dividing it by 65,we get 40 as remainder and hence the answer.

Is this solution Helpfull? Yes (3) | No (1)  

Shivam Khare  (6 years ago)

here d1=13 r1=1
d2=5 r2=3
when a number is divided by product of divisors , the remainder is d1(r2) + r1
therefore remainder = 13*3 + 1= 40

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Shalu  (6 years ago)

let N be the number.
so,
N=13*q+1
N=5*q1+3

N=1,14,27,40,53(by using n=13*q+1)
N=3,8,13,18,23,,28,33,38,43,48,53(by using n=5*q1+3)

common value is=53
N=lcm(13,5)*q+53
N=(65q+53)/65
reminder =53

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ajeet kumar pal  (5 years ago)

N/13=1(rem.)......(1)
N/5=3(rem.).........(2)
N=13*Q+1>>>>>(3)
put N value in 2 condition
13*Q+1/5
Q=3 then we get 40 but divisible by 65 (65>40)
Q=8 then we get 105/65
40(remainder)

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Abhinav kumar  (6 years ago)

let the no. 105, divided by 13, we get remainder 1 & quotient 8, 8 will be divided by 5, we get 3 as a remainder, therefore, if we divide 105 by 65, we get 40 as a remainder.

take another number, 170. divided by 13, we get remainder 1 & quotient 8, 8 will be divided
by 5, we get 3 as a remainder, therefore, if we divide 105 by 65, we get
40 as a remainder....

40 is right answer.

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shiv  (4 years ago)

--> 13(5x + 3) + 1
--> 65x + 40
--> rem = 40

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