Latest TCS Aptitude Question SOLUTION: A number when divided by 'D' leaves remainder of 8 and when divided by 3D leaves a remainder of 21.what is the remainder left,when twice of the number is divided by 3D. a-13 b-can

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A number when divided by 'D' leaves remainder of 8 and when divided by 3D leaves a remainder of 21.what is the remainder left,when twice of the number is divided by 3D.
a-13
b-can not be determined
c-3
d-42

Asked In TCS Vinay (12 years ago)

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riteshsingh  (12 years ago)

suppose the number is N and the quotient is Q and Q'.
now, N=DQ+8 ..(1)
N=3DQ'+21 ...(2)

now as we multiply the (1) by 3 and subtract it from (2) we would get
2N=3D(Q-Q')+3
hence the remainder is 3.

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jai Narayan Mishra  (12 years ago)

Let the number be n. Then there are integers p and q such that
n = pD + 8 (So 8 < D)...............(1)
and
n = 3qD + 21 (So 21 < 3D)........(2)

Thus
pD + 8 = 3qD + 21
(p - 3q)D = 13

Now since 13 is a prime, has just two divisors - namely 1 and 13 itself.
But from above, D > 1 which implies that p-3q = 1
Hence D = 13
which, from Eq(2) gives
n = 39q + 21
and
2n = 39*(2q) + 42
= 39*(2q + 1) + 3

So 2n has remainder 3 when divided by 3D = 39.

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