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

Question

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

Bunuel · Accepted Answer

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

BrentGMATPrepNow · Answer

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

RELATED VIDEO
 https://www.youtube.com/watch?v=XCxgIR042tE

GMATinsight · Answer

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  B

Abhishek009 · Answer

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)

ScottTargetTestPrep · Answer

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

BrushMyQuant · Answer

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

https://www.youtube.com/watch?v=P0S6j2uTaj4

bumpbot · Answer

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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

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