Divisibility

the attachments in this post are quite large. I am reattaching as word documents. Also, apologies for incorrectly putting this into the PS Forum

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?

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

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

I go with C as well,.. the remainder will be 6.

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

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