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## Kinh Nghiệm về What is the least possible number which when divided by 13 leaves a remainder 3 and when it is divided by 5 leaves a remainder 2? 2022

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When the positive integer n is divided by 3, the remainder i [#permalink]
23 May 2022, 01:03

When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n?

Math Review
Question: 15
Page: 220
Difficulty: medium

GRE Prep Club Legend

Joined: 10 Apr 2015

Posts: 6189

Re: When the positive integer n is divided by 3, the remainder i [#permalink]
23 May 2022, 06:02

Carcass wrote:

When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least
possible value of n?

When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

GIVEN: When the positive integer n is divided by 3, the remainder is 2
The
possible values of n are: 2, 5, 8, 11, 14, 17, 20,…

GIVEN: When n is divided by 5, the remainder is 1
The possible values of n are: 1, 6, 11, 16, 21,…

11 is the smallest value that appears in both lists of possible n-values.

Cheers,
Brent
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Brent Hanneson – founder of
Greenlight Test Prep

Intern

Joined: 25 Dec 2022

Posts: 12

Re: When the positive integer n is divided by 3, the remainder i [#permalink]
08 Jan 2022, 08:49

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. If n-2 is divisible by 5 and
t is divisible by 3. What is the remainder when the product nt is divided by 15 ?

a)0 b)1 c)2 d)3 e)5

Intern

Joined: 14 Mar 2022

Posts: 41

Re: When the positive integer n is
divided by 3, the remainder i [#permalink]
05 Apr 2022, 13:32

sandeep1995 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.
If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ?

a)0 b)1 c)2 d)3 e)5

can anyone solve this problem with a short trick?

Manager

Joined: 09 Mar
2022

Posts: 164

Re: When the positive integer n is divided by 3, the remainder i [#permalink]
05 Apr 2022, 22:25

asmasattar00 wrote:

sandeep1995 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. If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ?

a)0 b)1 c)2 d)3 e)5

can anyone solve this problem with a short trick?

You can use trail and error method.
The remainder is 1 when divided by 5, thus the number should be greater than multiple of 5 by 1.
5*1 = 5 + 1 = 6. On dividing with 5 gives remainder 1, but is perfectly divisible by 2. This does not satisfy the
condition.
5*2 = 10 + 1 = 11. And then divide the number by 3 to see if you get the remainder as 2. This satisfies the condition.

When the numbers are bigger, this method might be time consuming.

Intern

Joined: 14
Mar 2022

Posts: 41

Re: When the positive integer n is divided by 3, the remainder i [#permalink]
06 Apr 2022, 16:33

sandeep1995 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.
If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ?

a)0 b)1 c)2 d)3 e)5

is option A(0) is the right answer?

Manager

Joined: 09 Mar 2022

Posts: 164

Re: When the positive integer n is divided by 3, the remainder i [#permalink]
06 Apr 2022, 17:09

asmasattar00 wrote:

sandeep1995 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. If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ?

a)0 b)1 c)2 d)3 e)5

is option A(0) is the right answer?

Let’s try to solve n first. It is given that when n is divided by 3, we get 2 as remainder and also that n-2 must be divisible by 5. Start looking the table of 3, we can see that n can be 17, since 3*5 = 15 and when remainder is added, we get 17, plus n-2 = 15 is
divisible by 5.
For t, start with the table of 3, and we can see that when t=18, this is divisible by 3 and when it is divided be 5, you get a remainder of 3.
Hence, n=17 and t=18.
Thus, nt = 17*18 = 306.
On dividing it with 15, you should get 6 as remainder.
Please check if the options you’ve typed are correct.

Posted from my mobile device

Intern

Joined: 14 Mar 2022

Posts: 41

Re: When the positive integer n
is divided by 3, the remainder i [#permalink]
06 Apr 2022, 20:55

sukrut96 wrote:

asmasattar00 wrote:

sandeep1995 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. If n-2 is divisible by 5 and t is divisible by 3. What is the remainder when the product nt is divided by 15 ?

a)0 b)1 c)2 d)3 e)5

is option A(0) is the right answer?

Let’s try to solve n first. It is given that when n is divided by 3, we get 2 as remainder and also that n-2 must be divisible by 5. Start looking the table of 3, we can see that n can be 17, since 3*5 = 15 and when remainder is added, we
get 17, plus n-2 = 15 is divisible by 5.
For t, start with the table of 3, and we can see that when t=18, this is divisible by 3 and when it is divided be 5, you get a remainder of 3.
Hence, n=17 and t=18.
Thus, nt = 17*18 = 306.
On dividing it with 15, you should get 6 as remainder.
Please check if the options you’ve typed are correct.

Posted from my mobile device

thanks! I got your point , but for T I solve it as
t =3 , 3/3—-> fully divisible and 3/5—> remainder is 3

so 17*3=51
51/15 generates a remainder 6
once again thanks for your productive response

Senior Manager

Joined: 10 Feb 2022

Posts: 496

Re: When the positive integer n is divided by 3, the remainder i
06 May 2022, 08:59

GreenlightTestPrep wrote:

Carcass wrote:

When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the
remainder is 1. What is the least possible value of n?

When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

GIVEN: When the positive integer n is divided by
3, the remainder is 2
The possible values of n are: 2, 5, 8, 11, 14, 17, 20,…

GIVEN: When n is divided by 5, the remainder is 1
The possible values of n are: 1, 6, 11, 16, 21,…

11 is the smallest value that appears in both lists of possible n-values.

Cheers,
Brent

its easy to understand this rule, just one question, when we should apply this? because questions are
really different every time, so how to recognize where this rule will be applicable?
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When the positive integer n is divided by 3, the remainder i [#permalink]
03 Sep 2022, 22:26

Given that when n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. And we need to find the least possible value of
n

Theory: Dividend = Divisor*Quotient + Remainder

n is divided by 3, the remainder is 2

n -> Dividend
3 -> Divisor
a -> Quotient (Assume)
2 -> Remainders
=> n = 3*a + 2 = 3a + 2

n is divided by 5, the remainder is 1

=> n = 5b + 1 (Assume b is the quotient)

So, that value of n is possible which will satisfy both the conditions
=> n = 5b + 1 = 3a + 2
=> 5b = 3a + 2 – 1 = 3a +
1
=> b = (frac3a+15)
So, for b to be integer 3a + 1 should be a multiple of 5
a = 1, 3a + 1 = 3*1 + 1 = 4
a = 2, 3a + 1 = 3*2 + 1 = 7
a = 3, 3a + 1 = 3*3 + 1 = 10 => POSSIBLE

=> n = 3a + 2 = 3*3 + 2 = 11

Hope it helps!

Watch the following video to learn the Basics of Remainders

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### What is the maximum possible number which when divided by 13 leaves remainder 2?

By adding 15 we 9999 which when divided by 13 gives 9984 + 13 + 2 … a remainder of 2. Same Number when divided by 6 gives 9996+3 gives a remainder of 2. Hence conditions fulfilled. The number is 9999.

### What is the lowest number which leaves 3 as reminder when divided by 8 12 and 16?

The correct option is A 51.

### What is the smallest number that leaves a remainder of 2 when divided by 3?

Solution: The required number is 62.
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