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) cannot be determined c) 3 d) 42

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(#M40000879) TCS aptitude question Keep an EYE

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 Submited By-- tk (2 year ago)

Puzzle Status: Solved     By »» Mithila Nand Jha

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Mithila Nand Jha  (2 year 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 (140) | No (10)  

Sathish  (2 year 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 (47) | No (17)  

Arghadeep Chaudhury  (2 year 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 (9) | No (20)  

KALPANA G  (2 year 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 (4) | No (33)  

skyspy5  (7 Month 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 (2) | No (1)  

(#M40001551) TCS MATHS PUZZLE latest question Keep an EYE

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

Solution

let no be "a"..
a=Dx+8--------1
a=3Dy+21------2

D(x-3y)=13
.
. .x=4,y=1 nd D=13
sub D nd X in 1 thn a=60
twice-->2a=120
120 divided by 3D (13x 3)
120/39==> 3 ans
This answer is given by SOUJANYA ans is correct answer

Like manish sir answer on facbook.

Asked In tcs Submited By-- Aditi Sharma (1 year ago)

Puzzle Status: Solved

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Amit Singh  (1 year ago)

If Number is N and Divisor is D then from given conditions
N = a*D + 8 --- 1
N = b*3D + 21 --- 2

We have to find R
2N = c*3D + R

from (2)- (1) we get
D(3b - a) = 21 - 8 = 13

This implies D is a factor of 13
now D cannot be one therefore D=13

From 2
2N = 2b*3D + 21*2 --- (2)*2
= K*3D + 42
= K*3*(13) + 13*3 + 3 --as D=13
= (K + 1)3*13 + 3 -- Rearranging the Divisor part to insert 3*13
= c*3D + 3

Thus 2N = c*3D + 3
Hence remainder will be 3

For basic concept explanation please find a more complex sample with solution details
If there is Number N and Divisor D such that
N=aD + 17 -- 1
3N = bD +7 --2
What is R in below equation?
8N = cD + R
Solution:
Now from 3(1) - (2)
D(3a-b) = 17*3 - 7 = 44
==> D = 2,4,11,22,44
Remainder is 17 when N is divided by D
hence D cannot be less than 17
==> D= 22 or 44
Now
8N = 8aD + 8*17 -- from 8*(1)
= 8aD + 136

8aD is divisible by D so eliminated
Focus on 136 when divided by D (22 or 44)
Remainder(136/22) = Remainder(136/44) = 4
Hence
8N = 8aD + 4
OR
8N = cD + 4

8N = (8a + 3)D + 4 // In case of D=44
8N = (8a + 6)D + 4 // In case of D=22
This is basic funda
if case where D > 136 then remainder wud be 136 only
if case where D < 136 like here then aproach like above
--Amit Pratap Singh

Is this solution Helpfull? Yes (2) | No (10)  

SHRI KANT  (1 year ago)

answer will be 15

Is this solution Helpfull? Yes | No (4)  

(#M40002599) SELF MATHS PUZZLE Keep an EYE

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

Submited By-- aniruddha mandal (1 year ago)

Puzzle Status: Solved     By »» GAURAV TYAGI

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GAURAV TYAGI  (1 year ago)

making eqn as per the question
a=Dx+8......1
a=3Dy+21....2
multiplying 3 in eqn 1 we get eqn 3
3a=3Dx+24....3
a=3Dy+21......2
now subtract 2 from 3 we get..
2a=3D(x-y)+3
so here's the remainder we got is 3
so is the answer option c

Is this solution Helpfull? Yes (106) | No (4)  

udhaya  (1 year ago)

1)?assume D=13, we need remainder as 8 so 21/13=8 remainder.
2)then 3D leaves the remainder 21, so 21/3*13=21/39=21.
3)twice the remainder of 2 is divided by 3D, so 42/3*13=42=39=3

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baidyanath  (1 year ago)

analytic way as abhove one is very good trick
n=kD+8,D>8
n=3mD+21
subtract
we get,
d=13/k-3m
which is satify for d integer is (1,0)&(4,1)
choosing 1,0
D=13
ans=3
while chosin 4,1
ans=8
option given 3
so 3is ans

Is this solution Helpfull? Yes (6) | No (1)  

ANUJ MAURYA  (1 year ago)

Remainder = 3
let number is x,and quotient is A . D is divisor,and R is remainder= 8
then x = A*D + 8 --------------(I)
in second situation let quotient is B , 3D is divisor and R is remainder = 21
then x = B*3D +21 -----------(II)
from eq.(i)& eq.(ii)
AD +8 =3BD +21
or AD - 3BD =21 - 8 = 13
or D (A- 3B) =13*1
or D=13 ,and A -3B = 1 , IF B = 1 ,then A = 4
NUMBER X = 4*13 + 8 = 52+8 = 60
If 60*2 is divided by 3D =3*13 =39,
120/39 = 3 is quotient,and REMAINDER = 3 ANS.

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pavankumargvs  (1 year ago)

@baidyanath............ hai dude hav some dout........ equation for d will be satified for diffrent solution resulting it as integer u can try for (1,0)(4,1)(7,2) (10,3) and many more which gives on simplification of 2*x/3*d gives us 42/39 , 2.999, 198/39, 276/ 39...... as the values changing we will et several solution in which 2.99 will be some wht neare ........... i wil accept C..... but i think we cannot be determined is also acepted wht u wil say......?????

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(#M40002780) TCS MATHS PUZZLE apptitude Keep an EYE

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 Submited By-- harshit gupta (1 year ago)

Puzzle Status: Solved     By »» Ankit

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anvesh  (1 year ago)

x/d=8 and x/3d=21
3x/3d=24
(3x/3d)-(x/3d)=(24-21)=3

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soujanya  (1 year ago)

let no be "a"..
a=Dx+8--------1
a=3Dy+21------2

D(x-3y)=13
.
. .x=4,y=1 nd D=13
sub D nd X in 1 thn a=60
twice-->2a=120
120 divided by 3D (13x 3)
120/39==> 3 ans

Is this solution Helpfull? Yes (9) | No (2)  

Ankit  (1 year ago)

hey avinesh
x/d=8 means 8d=x its not give remainder
let the number be n so
n=Dx+8 ( x is quotient) ----1
n=3Dy+21(y is quotient) ----2
->D(x-3y)=13
so As 13 is prime number
there are two option D=1 and x-3y=13 or d=13 and x-3y=1
d is not = 1 as it give remainder
so D=13
x-3y=1
now we 1 is n=Dx+8
let x=4 and y=1
then from 1 n=60
when 60 divide by 13 give remainder 8
and when 60 divide by 39 give remainder 21
when 2n=120 divide by 3D=39 remainder= 3

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Abhishek Choudhary  (1 year ago)

option-c
solution

Is this solution Helpfull? Yes | No (5)  

Neetu shrivastava  (1 year ago)

c)3 is ans

Is this solution Helpfull? Yes | No (4)