Divisibility
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LSB
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the attachments in this post are quite large. I am reattaching as word documents. Also, apologies for incorrectly putting this into the PS Forum
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- Divisibility.doc
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parallel_chase
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n=3q+2
t=5q+3
nt = 15q + r ??
Statement I
n-2 is divisible by 5
n-2=5q+0
n=5q+2
We dont have any information about t, therefore insufficient.
Statement II
t is divisible by 3
we dont know anything about n
Insufficient.
Statement I & II
n=3q+2
n=5q+2
t=5q+3
t=3q+0
nt=15q+r
nt when divided by 15, t will be taken by 3 since it is divisible by 3, when n is divided by 5 the remainder will be 2.
Sufficient.
Hence C.
Whats the OA?
t=5q+3
nt = 15q + r ??
Statement I
n-2 is divisible by 5
n-2=5q+0
n=5q+2
We dont have any information about t, therefore insufficient.
Statement II
t is divisible by 3
we dont know anything about n
Insufficient.
Statement I & II
n=3q+2
n=5q+2
t=5q+3
t=3q+0
nt=15q+r
nt when divided by 15, t will be taken by 3 since it is divisible by 3, when n is divided by 5 the remainder will be 2.
Sufficient.
Hence C.
Whats the OA?
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sudhir3127
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I go with C as well,.. the remainder will be 6.LSB wrote:Thanks parallel_chase.
OA is C. Logic makes sense.
But when I picked numbers it did not work out.
Say
N = 17
T = 48
N*T= 816
816/15 = 54 R6
Not sure if Im missing something here
here it goes..
n=3x+2.................................................1
t=5y+3..................................................2
Statement 1:
from 1 we know
n-2=3x
this means 3x is divisible by 5
so let 3x=3*5*a=15a
equation (1) is now n=15a+2..............not sufficient
Statement 2:
t divisible by 3........ (t=5y+3 is divisible by 3)
which means 5y is divisible by 3
so assume 5y=3*5*b=15b
now is t=15b+3............not sufficient
combining 1 and 2
nt = (15a+2)*(15b+3)
= 225ab+45a+30b+6
=15[15ab+3a+2b]+6
thus we know from it that when nt is divided by 15 .. we will get 6 as remainder..
Hope that helps.. do let me know if u still have any doubts
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canuckclint
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Just need to do modular arithmetic, like equations:
The exact solution is:
Given 1: n = 2 (mod 3)
Given 2: t = 3 (mod 5)
Stmt 1: n-2 = 0 (mod 5)
Stmt 2: t = 0 (mod 3)
From Given 1, n = 2(mod 3) (Subtract 2 from both sides) gives:
n - 2 = 0 (mod 3)
n - 2 = 0 (mod 5) (Given 1)
If n-2 is divisible by 3 and 5, n-2 must be divisible by 15.
Similarly subtract 3 from both sides using of Given 2:
t - 3 = 0 (mod 5)
t - 3 = 0 (mod 3)
If t-3 is divisible by 3 and 5, t-3 must be divisible by 15.
So we have
n - 2 = 0 (mod 15)
t - 3 = 0 (mod 15)
n = 15 x + 2
t = 15 x + 3
n*t = 15^2 x + 5 (15x) + 6
Remainder is 6
The exact solution is:
Given 1: n = 2 (mod 3)
Given 2: t = 3 (mod 5)
Stmt 1: n-2 = 0 (mod 5)
Stmt 2: t = 0 (mod 3)
From Given 1, n = 2(mod 3) (Subtract 2 from both sides) gives:
n - 2 = 0 (mod 3)
n - 2 = 0 (mod 5) (Given 1)
If n-2 is divisible by 3 and 5, n-2 must be divisible by 15.
Similarly subtract 3 from both sides using of Given 2:
t - 3 = 0 (mod 5)
t - 3 = 0 (mod 3)
If t-3 is divisible by 3 and 5, t-3 must be divisible by 15.
So we have
n - 2 = 0 (mod 15)
t - 3 = 0 (mod 15)
n = 15 x + 2
t = 15 x + 3
n*t = 15^2 x + 5 (15x) + 6
Remainder is 6
