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When integer n is divided by 15, the remainder is 5. Which of the foll

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When integer n is divided by 15, the remainder is 5. Which of the foll [#permalink] New post   Updated on: 25 Jun 2015, 01:22
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When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III
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B

Originally posted by RudeyboyZ on 25 Jun 2015, 01:11.
Last edited by Bunuel on 25 Jun 2015, 01:22, edited 1 time in total.
Renamed the topic and edited the question.
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Re: When integer n is divided by 15, the remainder is 5. Which of the foll [#permalink] New post   25 Jun 2015, 01:29
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RudeyboyZ wrote:
When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III


When integer n is divided by 15, the remainder is 5: n = 15q + 5, so n can be 5, 20, 35, ...

I. 3n = 45q + 15 = 15(3q + 1) = {a multiple of 15}, thus it has the remainder of 0, when divided by 15.

II. 5n = 75q + 25 = 75q + 15 + 10 = 15(5q + 1) + 10 = {a multiple of 15} + 10, thus it has the remainder of 10, when divided by 15.

III. 4n + 10 = 60q + 20 + 10 = 60q + 30 = {a multiple of 15}, thus it has the remainder of 0, when divided by 15.

Answer: B.

P.S. Please name topics properly. Check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
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Re: When integer n is divided by 15, the remainder is 5. Which of the foll [#permalink] New post   29 Jan 2018, 07:59
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RudeyboyZ wrote:
When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III


Many integer properties questions can be solved by testing values

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.

When integer n is divided by 15, the remainder is 5.
So, some possible values of n are: 5, 20, 35, 50, 65, ....

Which of the following has a remainder of 10 when divided by 15 ?
Let's test a possible value of n.

Try n = 5
I. 3n = 3(5) = 15. When we divide 15 by 15, we get remainder 0. So, statement I does NOT satisfy the requirement.
ELIMINATE answer choices A, D and E

II. 5n = 5(5) = 25. When we divide 25 by 15, we get remainder 10. So, statement II DOES satisfy the requirement. This means we can't eliminate anything.

III. 4n + 10 = 4(5) + 10 = 30. When we divide 30 by 15, we get remainder 0. So, statement III does NOT satisfy the requirement.
ELIMINATE answer choice C

Answer: B

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When integer n is divided by 15, the remainder is 5. Which of the foll [#permalink] New post   25 Jun 2015, 02:44
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RudeyboyZ wrote:
When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III


Take any value of n which leaves remainder 5 when divided by 15

i.e. Let, n=20 (i.e.15+5)


I. 3n = 3*20 = 60 When divided by 15 remainder is NOT 10
II. 5n = 5*20 = 100 When divided by 15 remainder is 10
III. 4n + 10 = 4*20 + 10 = 90 When divided by 15 remainder is NOT 10

Answer: Option
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B
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Re: When integer n is divided by 15, the remainder is 5. Which of the foll [#permalink] New post   10 Jan 2022, 11:38
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When integer n is divided by 15, the remainder is 5

Theory: Dividend = Divisor*Quotient + Remainder

n -> Dividend
15 -> Divisor
a -> Quotient (Assume)
5 -> Remainders
=> n = 15*a + 5 = 15a + 5

Which of the following has a remainder of 10 when divided by 15

I. 3n
3n = 3*(15a + 5) = 45a + 15 = 15*(3a+1)
=> 3n when divided by 15 gives 3a+1 as quotient and 0 as remainder => FALSE

II. 5n
5n = 5*(15a + 5) = 75a + 25 = 75a + 15 + 10 = 15*(5a+3) + 10
=> 5n when divided by 15 gives 5a+3 as quotient and 10 as remainder => TRUE

III. 4n + 10
4n + 10 = 4*(15a + 5) + 10 = 60a + 20 + 10 = 15*4a + 30 = 15*(4a + 2)
=> 4n + 10 when divided by 15 gives 4a + 2 as quotient and 0 as remainder => FALSE

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders

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Re: When integer n is divided by 15, the remainder is 5. Which of the foll [#permalink] New post   27 Nov 2016, 01:18
RudeyboyZ wrote:
When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III


Least value of n = 20

Now chec the options

I. 3n = 60 ; 60/15 , Remainder is 0

II. 5n = 100 ; 100/15 ; Remainder is 10

III. 4n + 10 = 90 ; 90/15 , Remainder is 0

Hence, answer will be (B)
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Re: When integer n is divided by 15, the remainder is 5. Which of the foll [#permalink] New post   30 Jan 2018, 11:26
Expert Reply
RudeyboyZ wrote:
When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III


We can create the equation in which Q = quotient:

n = 15Q + 5

Let’s now analyze each Roman Numeral:

I. 3n

3n = 45Q + 15

(45Q + 15)/15 = 3Q + 1

We see that 3n is evenly divisible by 15, so the remainder is 0.

II. 5n

5n = 45Q + 25

(45Q + 25)/15 = (45Q + 15)/15 + 10/15 + 3Q + 1 + 10/15

We see that the remainder is 10, so II is true.

III. 4n + 10

4n + 10 = 60Q + 20 + 10 = 60Q + 30

(60Q + 30)/15 = 4Q + 2

We see that 4n + 10 is evenly divisible by 15, so the remainder is zero.

Answer: B
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Re: When integer n is divided by 15, the remainder is 5. Which of the foll [#permalink] New post   15 Apr 2023, 06:59
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Re: When integer n is divided by 15, the remainder is 5. Which of the foll [#permalink]
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