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When n is divided by 5 the remainder is 3. What is the remainder when

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Bunuel
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When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  21 Jul 2015, 03:11
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When n is divided by 5 the remainder is 3. What is the remainder when (n + 4)^2 is divided by 5?

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

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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  21 Jul 2015, 04:02
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Bunuel wrote:
When n is divided by 5 the remainder is 3. What is the remainder when (n + 4)^2 is divided by 5?

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

Kudos for a correct solution.


one possible value of n = 5+3 = 8

i.e. n+4 = 8+4 = 12

12^2 = 144

144 when divided by 5 leaves remainder 4

Answer: Option E
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  21 Jul 2015, 04:13
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Bunuel wrote:
When n is divided by 5 the remainder is 3. What is the remainder when (n + 4)^2 is divided by 5?

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

Kudos for a correct solution.


Let n =5q+3 ---> n =8 must satisfy the given question as n can be any number of the form n =5q+3

Thus rem when (8+4)^2 = 144 is divided bny 5 = 4. E is the correct answer.
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  21 Jul 2015, 07:42
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n must be of the form 5(x)+3, where x is an integer.

[(5x+3)+4]^2 = (5x+7)^2 = 25x^2 + 70x + 49.

For x = 1: 25(1) + 70(1) + 49 = 144.

Remainder when 144 is divided by 5 will be 4.

Hence, Ans (E).
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  21 Jul 2015, 09:24
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Bunuel wrote:
When n is divided by 5 the remainder is 3. What is the remainder when (n + 4)^2 is divided by 5?

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

Kudos for a correct solution.


I plugged in n=8. (When dividing 8/5 = 1 and Remainder is 3)

Now plug in 8 in (n + 4)^2 >>> 12^2/5 = 28 with a remainder of 4

Answer E
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  21 Jul 2015, 09:31
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Bunuel wrote:
When n is divided by 5 the remainder is 3. What is the remainder when (n + 4)^2 is divided by 5?

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

Kudos for a correct solution.


The first sentence says:
n=5x+3

Therefore, n can be 3, 8, 13, etc.

(3+4)^2 = 49, remainder is 4.
(8+4)^2 = 144, remainder is 4.

E
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  25 Jul 2015, 00:54
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You don't need to plug in values.

question is for (n+4) ^ 2:

let n = 5k + 3.

Add 4 to RHS & LHS => n+4 = 5k + 3 + 4 => n+4 = 5k + 5 + 2 . Here you can see 5k + 5 is divisible by 5.

Now square RHS & LHS => (n+4)^2 = (5k + 5 + 2)^2. For ease let 5k+5 be X which is anyway divisible by 5
=> (n+4)^2 = (X+ 2)^2
=> (n+4)^2 = X^2 + 4 +2X

When we divide X^2 + 4 +2X by 5 ... X^2 & 2X are divisible by 5.
So 4 remains to be divided by 5 .

Hence remainder is 4 ie Ans : E
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  25 Jul 2015, 03:31
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Bunuel wrote:
When n is divided by 5 the remainder is 3. What is the remainder when (n + 4)^2 is divided by 5?

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

Kudos for a correct solution.


n can be 3,8,13,18 and so on

(n+4)^2=49,144,289 and so on.
Remainder =4 when divided by 5
Answer E
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  26 Jul 2015, 12:25
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Bunuel wrote:
When n is divided by 5 the remainder is 3. What is the remainder when (n + 4)^2 is divided by 5?

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

Kudos for a correct solution.


800score Official Solution:

When n is divided by 5 the remainder is 3. So n = 5k + 3, where k is some non-negative integer. (n + 4)² = (5k + 7)² = 25k² + 70k + 49 = 5(5k² + 14k + 9) + 4. Therefore when (n + 4)² is divided by 5 the remainder is 4. The right answer is (E).

Another option is to plug in n = 3. We can do so under an assumption that the remainder must be the same for ANY n, which yields 3 as the remainder when divided by 5.
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  06 Apr 2018, 11:39
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n = 5+3 = 8

i.e. n+4 = 8+4 = 12

12^2 = 144

E
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  08 Apr 2018, 06:49
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one possible value of n = 5+3 = 8

i.e. n+4 = 8+4 = 12

12^2 = 144

144 when divided by 5 leaves remainder 4

Answer: Option E
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  28 Feb 2020, 15:22
Expert Reply

Solution


    • When n is divided by 5 the remainder is 3

To find
    • The remainder when (n + 4)^2 is divided by 5

Approach and Working out
    • (n+4)^2 = n^2 +16 +8n
    • (n^2 +16 +8n /5)R = (n^2/5)R + (16/5)R + (8n /5)R
    • = (9/5)R + 1 + (24/5)R
    • =(4 +1 +4/5)R =(9/5)R
    • = 4

Hence, option E is the correct answer.

Correct Answer: Option E
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  28 Feb 2020, 20:36
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Since it is a PS question, it will have a unique answer for any n which gives the remainder of 3 when divided by 5.

So, we can take any n which gives the remainder of 3 when divided by 5.
Let us take the smallest positive n = 3
Now, (n + 4)^2 = (3+4)^2 = 49
49/5 remainder = 4

Answer = E


Bunuel wrote:
When n is divided by 5 the remainder is 3. What is the remainder when (n + 4)^2 is divided by 5?

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

Kudos for a correct solution.

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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  29 Mar 2020, 03:49
Bunuel wrote:
When n is divided by 5 the remainder is 3. What is the remainder when (n + 4)^2 is divided by 5?

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

Kudos for a correct solution.


Given: When n is divided by 5 the remainder is 3.

Asked: What is the remainder when (n + 4)^2 is divided by 5?

n = 5k + 3
n+4 = 5k + 3 + 4 = 5(k+1) + 2

(n+4)^2mod5 = 2^2mod5 = 4

IMO E
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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink] New post  12 Feb 2022, 08:01
N/5 R 3
(N+4)/5 R 2
(N+4)/5. X (N+4)/5 reminder 2x2 = 4

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Re: When n is divided by 5 the remainder is 3. What is the remainder when [#permalink]
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