Elitmus
Exam
Numerical Ability
Number System
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
Read Solution (Total 7)
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- 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 - 7 years agoHelpfull: Yes(29) No(0)
- 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.
- 7 years agoHelpfull: Yes(3) No(1)
- 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 - 7 years agoHelpfull: Yes(1) No(0)
- 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 - 7 years agoHelpfull: Yes(1) No(2)
- 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) - 6 years agoHelpfull: Yes(1) No(0)
- 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. - 7 years agoHelpfull: Yes(0) No(0)
- --> 13(5x + 3) + 1
--> 65x + 40
--> rem = 40 - 5 years agoHelpfull: Yes(0) No(0)
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