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Numerical Ability
Number System
A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21. What is the remainder left, when twice the number is divided by 3D?
a) 13
b) cannot be determined
c) 3
d) 42
Read Solution (Total 9)
-
- let's number is n
so n=Dx+8------->1
n=3Dy+21--------->2
from 1 & 2 D(x-3y)=13
here 13 is prime number so it has factors 1 and 13 only
x-3y must be 1
let x=4 and y=1
then n=60
so 2n is divided that is 120 by 3D that is by 39 we get
the remainder as 3 - 14 years agoHelpfull: Yes(178) No(16)
- Let the number be n
Given its divided by D and leaves remainder 8. Lets assume the quotient be x. So that
n=Dx+8
Similarly n when divided by 3D leaved remainder 21. Lets assume the quotient be y. So that
n=3Dy+21
Equating the above 2, we get
Dx+8 = 3Dy+21
Dx-3Dy=21-8
D(x-3y) = 13
Since 13 is a prime number and according to the above equation, D and x-3y when multiplied should give me 13
The only two factors of 13 are 1 and 13
So if D is 1, x-3y is 13
If D is 13, x-3y is 1
D can never be 1 because given the number leaves remainder when divided by D. No number can leave remainder whe - 14 years agoHelpfull: Yes(66) No(21)
- i think ans must be b) cant be determind. bcz D(x-3y)=13 and d must be 13. it cant be 1. now (x-3y)=1 and in order to satisfy this result it is possible to choose any arbitay value of x & y.(eg. x=4 y=1,x=7 y=2,x=9 y=3 and so on)and for each time we get a new value of reminder. therefore ans must be (b).
- 14 years agoHelpfull: Yes(14) No(27)
- let the number be N.
From the Given that, it is understood that
(N/D) + 8 = (N/3D)+27
=> N/D - N/3D =27-8
=>2N/3D =13, hence the answer is 13. - 9 years agoHelpfull: Yes(9) No(5)
- by using division rule, x=dp+r, where d is +ve integer, p is quotient and integer,and r is reminder and 0(1),
x=3Dq+21 -------->(2), where p and q are Quotients.
From (1) & (2), D(p-3q)=13,
we know that 13 is prime number.
so, factors of 13 are only 1 & 13.
therefore D=13 & p-3q=1 ( From (A), 8 - 14 years agoHelpfull: Yes(5) No(37)
- acc to given (n-8)/d and (n-21)/3d will nt leave any remainder...
So, multiply 1st by 3 and devide by 3 and then subtract 2nd from 1st.
we get
3(n-8)/3d - (n-21)/3d = (2n-3)/3d....from the ans. we get remainder ==3 when 2n is devided by 3d
- 12 years agoHelpfull: Yes(4) No(1)
- pls check calculation @ mithila nand jha ...when we divide 120/39 then we get remainder as 1.
your process is correct.
- 9 years agoHelpfull: Yes(0) No(1)
- #jyoti 120/39 gives rem as 3 not 1
- 7 years agoHelpfull: Yes(0) No(0)
- my ans is = 13
- 5 years agoHelpfull: Yes(0) No(0)
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