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When integer n is divided by 15, the remainder is 5. Which of the foll  [#permalink]

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Question Stats: 72% (01:46) correct 28% (01:59) wrong based on 257 sessions

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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

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]

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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.

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When integer n is divided by 15, the remainder is 5. Which of the foll  [#permalink]

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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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Re: When integer n is divided by 15, the remainder is 5. Which of the foll  [#permalink]

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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

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]

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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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Re: When integer n is divided by 15, the remainder is 5. Which of the foll  [#permalink]

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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

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] 10 Feb 2019, 19:11
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