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# Positive integer n is divisible by 5. What is the remainder when

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Math Expert
Joined: 02 Sep 2009
Posts: 44566
Positive integer n is divisible by 5. What is the remainder when [#permalink]

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22 Jul 2015, 02:06
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Question Stats:

79% (00:48) correct 21% (00:47) wrong based on 159 sessions

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Positive integer n is divisible by 5.
What is the remainder when dividing 4(n + 1)(n + 8) by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: Positive integer n is divisible by 5. What is the remainder when [#permalink]

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22 Jul 2015, 04:47
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Let n = 5.

4 * 6 * 13 = 312, which leaves a remainder of 2 when divided by 5. Ans (C).
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Posts: 117
Schools: HBS '18, IIMA
Re: Positive integer n is divisible by 5. What is the remainder when [#permalink]

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22 Jul 2015, 06:41
1
KUDOS
Bunuel wrote:
Positive integer n is divisible by 5.
What is the remainder when dividing 4(n + 1)(n + 8) by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Kudos for a correct solution.

Solution -
Given that Positive integer n is divisible by 5.

4(n + 1)(n + 8)/5 = (4n+4)(n+5+3)/5 -->4n and n+5 are divisible by 5, so remaining part is 4*3/5 = 12/5 --> Remainder is 2
ANS C.
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Math Expert
Joined: 02 Aug 2009
Posts: 5769
Re: Positive integer n is divisible by 5. What is the remainder when [#permalink]

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22 Jul 2015, 06:53
1
KUDOS
Expert's post
Bunuel wrote:
Positive integer n is divisible by 5.
What is the remainder when dividing 4(n + 1)(n + 8) by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Kudos for a correct solution.

two ways..
1) substitute n as 5, 4*6*13.. last digit is 2 , so remainder=2..
2) 4leaves a remainder 4, n+1 will leave 1 and n+8,8 .. so remainder=4*1*8=32 or 2
ans C
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Re: Positive integer n is divisible by 5. What is the remainder when [#permalink]

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22 Jul 2015, 06:56
Bunuel wrote:
Positive integer n is divisible by 5.
What is the remainder when dividing 4(n + 1)(n + 8) by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Kudos for a correct solution.

Given : Possible values of n = 5, 10, 15, 20, 15, 20, 25, .... etc = 5a

Question : Remainder when 4(n + 1)(n + 8) is divided by 5 = ?

CONCEPT: (Remainder when a is divided by x)*(Remainder when b is divided by x) = (Remainder when a*b is divided by x)
Also (Remainder when a is divided by x)+(Remainder when b is divided by x) = (Remainder when {a+b} is divided by x)

Method-1

i.e. Remainder [$$\frac{4(n + 1)(n + 8)}{5}$$] = 4*Remainder [$$\frac{(n + 1)}{5}$$]*Remainder [$$\frac{(n + 8)}{5}$$]

i.e. Remainder [$$\frac{4(n + 1)(n + 8)}{5}$$] = 4*Remainder [$$\frac{(5a + 1)}{5}$$]*Remainder [$$\frac{(5a + 8)}{5}$$]

i.e. Remainder [$$\frac{4(n + 1)(n + 8)}{5}$$] = 4*1*Remainder [$$\frac{(8)}{5}$$] = 4*1*3 = 12

i.e. Remainder [$$\frac{4(n + 1)(n + 8)}{5}$$] = Remainder (12/5) = 2

Method-2

Let, n=5

then, 4(n + 1)(n + 8) = 4(5 + 1)(5 + 8) = 4*6*13 = 312

i.e. Remainder [$$\frac{4(n + 1)(n + 8)}{5}$$] = i.e. Remainder [$$\frac{312}{5}$$] = 2

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Re: Positive integer n is divisible by 5. What is the remainder when [#permalink]

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22 Jul 2015, 07:05
1
KUDOS
Bunuel wrote:
Positive integer n is divisible by 5.
What is the remainder when dividing 4(n + 1)(n + 8) by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Kudos for a correct solution.

Let n=15
Then, 4(16)(23)=1472
1472 by 5, remainder=2
Manager
Joined: 20 Jul 2011
Posts: 80
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Re: Positive integer n is divisible by 5. What is the remainder when [#permalink]

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22 Jul 2015, 13:06
1
KUDOS
Bunuel wrote:
Positive integer n is divisible by 5.
What is the remainder when dividing 4(n + 1)(n + 8) by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Kudos for a correct solution.

Let n = 5
4(n + 1)(n + 8) ;Here, the unit digit is the remainder when divided by 5
4 * 6 * 13 = **2

Option C
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Re: Positive integer n is divisible by 5. What is the remainder when [#permalink]

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22 Jul 2015, 16:52
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Here is what I did-

Option 1) Picked up some sample numbers (5,15,20) and tried out the multiplication. Each time remainder is 2

Option 2) As n is divisible by 5 - it can only end in 5 or 0. Based on this:
a) n+1 can end in 6 or 1
b) n+8 can end in 1 or 8

When we multiply each of these options 4*6*3 OR 4*1*8 --> we get numbers ending in 2. When divided by 5 any number ending in 2 will always give 2 as remainder.

Hope this is the correct way to solve this one.

Thanks!
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Math Expert
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Posts: 44566
Re: Positive integer n is divisible by 5. What is the remainder when [#permalink]

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26 Jul 2015, 11:57
Bunuel wrote:
Positive integer n is divisible by 5.
What is the remainder when dividing 4(n + 1)(n + 8) by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Kudos for a correct solution.

800score Official Solution:

Let’s simplify 4(n + 1)(n + 8) = 4(n² + 9n + 8) = 4n² + 36n + 32. Or we can put it in this way:
4(n + 1)(n + 8) = (4n² + 36n + 30) + 2.

n is divisible by 5 and 30 is also divisible by 5 so (4n² + 36n + 30) is divisible by 5. Therefore 2 is the remainder when dividing 4(n + 1)(n + 8) by 5. The correct answer is C.

An alternative way to solve this is to plug in numbers for n and you would be able to arrive at the answer.
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Re: Positive integer n is divisible by 5. What is the remainder when [#permalink]

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20 Mar 2018, 15:57
Bunuel wrote:
Positive integer n is divisible by 5.
What is the remainder when dividing 4(n + 1)(n + 8) by 5?

A. 0
B. 1
C. 2
D. 3
E. 4

Kudos for a correct solution.

Number divides by 5 when tends with 0 or 5

Let x =5

4(n + 1)(n + 8) = 4 * 6 * 8 = XY2...............No need to calculate. Use the unit digit.

Let x = 10 (just for confirmation)

4(n + 1)(n + 8) = 4 * 11 * 18 = XY2

This means the number end with 2 above the number ends with 0...Then reminder is 2

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Posts: 25
Re: Positive integer n is divisible by 5. What is the remainder when [#permalink]

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08 Apr 2018, 07:14
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Let n = 5.

4 * 6 * 13 = 312, which leaves a remainder of 2 when divided by 5. Ans (C).
Re: Positive integer n is divisible by 5. What is the remainder when   [#permalink] 08 Apr 2018, 07:14
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