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Question

I have asked this question earlier also but forgotten the explanation. pls tell a shortcut 2 solve this

scthakur · Answer

From stmt1: n = 5a + 2
From stmt2: t = 3*5b + 3 = 15b + 3

Hence, nt = 75ab + 30b + 15a + 6

Thus, when nt is divided by 15, the remainder will be 6.

ritula · Answer

Can u pls explain how u got this? (highlighted in red)

x2suresh · Answer

n=3k+2 -->(1)
t=5l+3 -->(2)
 
 stat1: 
 n-2 = 5m 
 n=5m+2 -->(3)
 from (1) and (2) it is clear 
 3k=5m
 
 --> n= 15*a+2
 
 stat2:
 t=3x -->(4)
 
 from (4) and (2)
 
 3x=5l+3 ---> 5l must be multiple of 3
 5l= 15b
 
 t= 15b+3

nt = (15*a+2)*(15b+3) = ...(multiple of15)+6
 remainder is 6

mrsmarthi · Answer

IMO C. The two solutions posted were saying the value of the remainder to be 6 but since it is a DS question we need not find the value. :wink:

Here is my approach. Given in the question stem, n - 2 is divisible by 3 since n is divisible by 3 leaving a remainder 2. -which means n-2 has atleast 3 as a factor ---fact 1 t - 3 is divisible by 5 since t is divisible by 5 leaving a remainder 3 - which mean t-3 has atleast 5 as a factor. ---fact 2 From stmt 1 , it is said that n-2 is divisible by 5. Which means n-2 has atleast 5 as a factor. And from fact 1, we know that 3 is factor of n-2. So we can conclude that n-2 has atleast 3 and 5 as factors or in other words n-2 = 15k where k is an interger. ==> n = 15k + 2 -----Eq 1 No additional information abt t. Hence insufficient. From stmt 2 , t is a divisible by 3, then t-3 is also divisible by 3. from fact 2, we know that t-3 has 5 also a factor. So we can conclude that t-3 has atleast 3 and 5 as factor or in other words, t-3 = 15l where l is an integer ==> t = 15l + 3 -----Eq 2. No additional information abt n is given. Hence insufficient Now combine both the statements, we know that n = 15k + 2 t = 15l + 3. Rule to remember - Arithmatic on remainders when divisiors are same states that when a and b are the remainders when x and y are divided by asome number n, then remainder left when product xy is divided by n is nothing but the product of the remainders a and b. Here n and k are numbers divided by 15 leaving remainders 2 and 3. So we can easily apply the above rule to find the remainder when product nt is divided by 15. So ans is C.

ritula · Answer

Superb! +1 frm me
pls edit ur post here(highlighted in red)
1 more thing can u pls tell sum source where these rules can be learnt bcos i wasnt aware that such rule exists.

Ibodullo · Answer

Great Explanation! Agreed with C.

mrsmarthi · Answer

Ritula,

When ever I find some useful shortcuts which simplifies the process, I make a note on that(In other words an entry into flash card). So I didn't remember the source of the rule that I mentioned. But probably it could be MGMAT - Number porperties Strategy guide. 
 
BTW, thanks for pointing out the mistake. I have edited the post.

walker · Answer

Another approach.

Let's write out a few possible values of n and t.
n e {2,5,8,11,14,17,20...}
t e {3,8,13,18,23,28...}

1) first condition limits possible values of n: n e {2,17...}
Let's check remainders for a couple of nt numbers at different t: n=2,t=3 --> r=6; n=2,t=8 --> r=1 - insufficient

2) second condition limits possible values of t: t e {3,18...}
Let's check remainders for a couple of nt numbers at different n: n=2,t=3 --> r=6; n=5,t=3 --> r=0 - insufficient

1)&2) first condition limits possible values of n: n e {2,17...} and second condition limits possible values of t: t e {3,18...}

Let's check remainders for a couple of nt numbers at different n and t:
n=2,t=3 --> r=6;
n=2,t=18 --> r=6;
n=17,t=3 --> r=6; - sufficient

This approach is a bit longer but it is always better to have a few approaches in a belt...

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