This solution is only detailed for better understanding. Hope it helps....

n = 3a + 2
t = 5b + 3
What is the remainder when nt/15?

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

1) n - 2 is divisible by 5.

n = 3a + 2
n - 2 = 3a
3a is divisible by 5 and therefore by 15

nt = 3a(5b + 3) + 2(5b + 3)
=15ab + 9a + 10b + 6
15ab and 9a are divisible by 15,
10b: no info from (1)
INSUFFICIENT

2) t = 5b + 3,
so 5b is divisible by 3 and therefore, by 15.

nt = 15ab + 9a + 10b + 6
10b is divisible by 15
15ab and 9a: no info from (2)
INSUFFICIENT

When you combine (1) and (2)...
15ab, 9a, and 10b are divisible by 15.
Therefore, nt = 15ab + 9a + 10b + 6
=15(x) + 6

C.

I looked at option 2 first.
The question can be re-written as (NT/5*3).
according to option 2, t is divisible by 3. But we can not tell if N will be divisible by 5 or not......insuff.

Lets analyse option 1.
NT can be written as (N-2+2)T which is (N-2)T + 2T.
So NT/15 = ((N-2)T + 2T)/15 or (N-2)T/5*3 + 2T/5*3
There is no way you can determine the divisibilty of T.......insuff.

If u combine 1 & 2 u know that T is divisible by 3 but there will be a 2/5 factor remaining which indicates that NT is not completely divisible by 15. Thats what we are looking for..........
Correct me if i went wrong...

I tried to proceed in this way:
n = 3a+2
t = 5b+3
So nt = 15ab+9a+10b+6 .... no use

Stmt1: if n-2 = 5x so, n = 5x+2. Now plugged in n = 17. Remainder will be 2 while divided by 15.....
Hence, n = 15M + 2

Stmt2: if t = 3y plugged in 18 and the remainder is 3 while divided by 15
Hence, t = 15N +3

stmt 1+ stmt 2: nt = (15M+2)*(15N+3)..... remainder is 6 ....suffice

...but this way it's too much confusing and time consuming....do you suggest any other way?
_________________

If You're Not Living On The Edge, You're Taking Up Too Much Space

Picking number may be confusing and intimidating. so solving equation would be best.
_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Please see above for the solutions - the OA is C, and the remainder is 6.
Great little problem!

what's up guys? i too originally missed this question during a practice exam. However, after reviewing it without time constraints, I realized that even when you don't understand a DS problem, always employ logic if you have to guess.

from the stem, given:

n= 3x+2
t= 5y+3

the best approach i discovered is simply to algebraically determine what n and t are in order to determine what the remainder of nt is

(i) given (n-2)/5 which can be expressed as n-2 = 5x
-now solve for n using the equation for n as given in the stem and substitute for x using (i)

n-2= 5x, x= (n-2)/5, now plugging into n as given in stem:
n = 3((n-2)/5)+2 this solves for n = 2. However, since not given anything for t, can eliminate A&D


(ii) now, in this statement, t is divisible by 3 can be written as t = 3y

-now plugging in this equation into the equation given in the stem ( t = 5y+3) and substituting y = t/3 as given in (ii): t = 5(t/3) +3.......solving for this equation yields t=-9/2. However, this statement gives nothing about n as required to solve for the remainder of nt/15. Hence, we can eliminate B.

now combined: n=2 and t= -9/2.........nt = -9

no need to solve for remainder! However, if you chose to calculate, you would soon realize that the remainder is 0. Try it and see for yourself.....


According to sojafon: nt = 15ab + 9a + 10b + 6. However, ab+9a+10b is not equal to X from a distributive property standpoint as assumed by 15X+6. Therefore the remainder is not 6 as assumed.

This is the only true and proven method I can see to be employed in order to solve this problem. However, if you were to employ a systematic approach, you will see that (i) gives nothing about t, which means eliminate AD. And (ii) says nothing about n, eliminate B. This leaves you with a 50/50 guess for C or E.

OA is C.

I used the same method as priyankur_saha. I think the answer is C.

Also if using numbers , N=17 and T =18 remainder is 6. The only problems with plugging in numbers is that you are not sure if the number you picked represent all cases. So although the first method is longer, I would prefer it over the number plugging way. However, on the test, if you don't have the time to invest, use 17 and 18.
_________________

Dream the impossible and do the incredible.

Live. Love. Laugh.

I agree that the answer is C. I solved it using the algebraic approach, but again... this is not a very fast approach.

From the problem statement we know:
n=3*x+2
t=5*y+3

Statement 1:

n-2=5*x
n=5*x+2

Plug into nt/15:
(5x+2)*(5y+3)/15

NOT SUFFICIENT --> There is no way to isolate a portion that is not divisible by 15.

Statement 2:

t=3*y

Plug into nt/15:

(3x+2)(3y)/15

NOT SUFFICIENT --> There is no way to isolate a portion that is not divisible by 15.

Statement 1 and 2:

(5x+2)(3y)/15
(15xy+6y)/15

If 6y/15 has a constant remainder than we can answer the question:

6*1/15 --> R=6
6*2/15 --> R=12
6*3/15 --> R=3
6*4/15 --> R=9
6*5/15 --> R=0
6*6/15 --> R=6
6*7/15 --> R=12
6*8/15 --> R=3

As you can see, the remainder is different values, but if you remember from the original problem statement. You can see that when t is divided by 5, the remainder must be 3:

6*1/15 --> R=6 because 3*1/5 has R=3
6*6/15 --> R=6 because 3*6/5 has R=3

Therefore the answer is C and the remainder is 6.

ya C. And just picking numbers seemed easier to me

I think you mean the divisor, not the dividend.