Latest TCS Aptitude Question SOLUTION: 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) ca

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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

Asked In TCS tk (14 years ago)

Solved Mithila Nand Jha Read Solution (9)

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Read Solution (9) :

Mithila Nand Jha  (14 years ago)

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

Is this solution Helpfull? Yes (178) | No (16)  

Sathish  (14 years ago)

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

Is this solution Helpfull? Yes (66) | No (21)  

Arghadeep Chaudhury  (14 years ago)

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).

Is this solution Helpfull? Yes (14) | No (27)  

ashwini k  (9 years ago)

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.

Is this solution Helpfull? Yes (9) | No (5)  

KALPANA G  (14 years ago)

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

Is this solution Helpfull? Yes (5) | No (37)  

skyspy5  (12 years ago)

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

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

jyoti kumari  (9 years ago)

pls check calculation @ mithila nand jha ...when we divide 120/39 then we get remainder as 1.
your process is correct.

Is this solution Helpfull? Yes | No (1)  

Nithin  (7 years ago)

#jyoti 120/39 gives rem as 3 not 1

Is this solution Helpfull? Yes | No   

Tanu Agrawal  (5 years ago)

my ans is = 13

Is this solution Helpfull? Yes | No   

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