[email protected] wrote:When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

(1) n-2 is divisible by 5.
(2) t is divisible by 3.

My approach to this question was:

1) N= 3k+2, so N can be 2, 5, 8, 11 and so on
2) when positive integer t is divided by 5 the remainder is 3= N=5Q+3, so t can be 3,8, 13, 18 and so on.

Stmnt 1 says n-2 is divisible by 5, that is for example 17-2 =15 and 32 -2 is 30 not sufficient
Stmnt 2 says t is divisible by 3 so it can be 18 or 33

Now if we combine the two Im getting multiple solutions so the answer should be E but the answer is C

Need clarity!

Shibsriz,
What are all the multiple solution u r getting could you please post.

Thanks in advance.
Regards,
Uva.

[email protected] wrote:When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

(1) n-2 is divisible by 5.
(2) t is divisible by 3.

My approach to this question was:

1) N= 3k+2, so N can be 2, 5, 8, 11 and so on
2) when positive integer t is divided by 5 the remainder is 3= N=5Q+3, so t can be 3,8, 13, 18 and so on.

Stmnt 1 says n-2 is divisible by 5, that is for example 17-2 =15 and 32 -2 is 30 not sufficient
Stmnt 2 says t is divisible by 3 so it can be 18 or 33

Now if we combine the two Im getting multiple solutions so the answer should be E but the answer is C

Need clarity!

Shibriz,
What you solved is correct.
From statement 1 you ended with 17 and 32
if you divide both by 15 you can see remainder as 2

From Statement 2 you ended with 18 and 33
If you divide both by 15 you can see remainder as 3

so combining 1 and 2

(15n+2)(15t+3)/15 will always get remainder as 6.

Hence Sufficient.


Regards,
Uva.

When positive integer N is divided by 3, the remainder is 2; and when positive integer T is divided by 5, the remainder is 3. What is the remainder when the product NT is divided by 15?

I) n-2 is divisible by 5
II) t is divisible by 3

OA to follow shortly

N is 2 more than a multiple of 3 = 2, 5, 8, 11, 14, 17...
T is 3 more than a multiple of 5 = 3, 8, 13, 18, 23, 28...

Statement 1: N is 2 more than a multiple of 5 = 2, 7, 12, 17, 22...
Numbers common to both lists for N = 2, 17...
Our original list for T = 3, 8, 13, 18, 23, 28...
Possible remainders when NT is divided by 15:
(2*3)/15 = 0 R6
(2*8)/15 = 1 R1
Since R=6 and R=1, insufficient.

Statement 2: T is a multiple of 3 = 3, 6, 9, 12, 15, 18...
Numbers common to both lists for T = 3, 18...
Our original list for N = 2, 5, 8, 11, 14, 17...
Possible remainders when NT is divided by 15:
(2*3)/15 = 0 R6
(5*3)/15 = 1 R0
Since R=6 and R=0, insufficient.

Statements 1 and 2:
Our final list for N = 2, 17...
Our final list for T = 3, 18...
Possible remainders when NT is divided by 15:
(2*3)/15 = 0 R6
(2*18)/15 = 2 R6
(17*3)/15 = 3 R6
(17*18)/15 = 20 R6

Since in each case R=6, sufficient.

The correct answer is C.