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

Question

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 .

TimeTraveller · Answer

Let n = 5.

4 * 6 * 13 = 312, which leaves a remainder of 2 when divided by 5. Ans (C).

balamoon · Answer

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.

chetan2u · Answer

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

GMATinsight · Answer

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

Answer: option C

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

Answer: option C

KS15 · Answer

Let n=15
Then, 4(16)(23)=1472
1472 by 5, remainder=2
Answer C

ashokk138 · Answer

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

aimtoteach · Answer

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.

Hence answer is C

Hope this is the correct way to solve this one.

Thanks!

Bunuel · Answer

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.

Mo2men · Answer

Number divides by 5 when tends with 0 or 5

Let x =5

4(n + 1)(n + 8) = 4 * 6 * 8 = XY  2  ...............No need to calculate. Use the unit digit.

Let x = 10 (just for confirmation)

4(n + 1)(n + 8) = 4 * 11 * 18 = XY  2

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

Answer: C

SidKan · Answer

Let n = 5.

4 * 6 * 13 = 312, which leaves a remainder of 2 when divided by 5. Ans (C).

ankushsambare · Answer

Good solution. Here’s a simpler version:
Let ( n = 0 ) (since 0 is divisible by 5).
Substitute into ( 4(n+1)(n+8) ):
( 4(1)(8) = 32 )
Now divide 32 by 5 
→ remainder is 2.

Answer: Option C

shahsahil2101 · Answer

4(n^2 + 9n + 8)= (4n^2 + 36n + 32)/5
The first two terms are divisible by 5, 32 is not and hence remainder is 2

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

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

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