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If x is a positive integer and x + 2 is divisible by 10, what is the

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If x is a positive integer and x + 2 is divisible by 10, what is the  [#permalink]

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New post 22 Aug 2018, 02:07
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If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x^2 + 4x + 9 is divided by 10?

A. 1
B. 3
C. 5
D. 7
E. 9
Spoiler: OA

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Re: If x is a positive integer and x + 2 is divisible by 10, what is the  [#permalink]

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New post 22 Aug 2018, 02:14
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Since X is a positive integer and x+2 is divisible by 10 then x can taje values 8,18,28,38....

For all these values of x, the remainder when x^2+4x+9 is divisible by 10 is 5.
For example, let's take x as 8
Then x^2+4x+9 = 64+32+9 = 105.
When 105 is divided by 10. Reaminder is 5

C is the answer.

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If x is a positive integer and x + 2 is divisible by 10, what is the  [#permalink]

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New post 22 Aug 2018, 02:15
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Bunuel wrote:
If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x^2 + 4x + 9 is divided by 10?

A. 1
B. 3
C. 5
D. 7
E. 9


\(x^2 + 4x + 9\) can be written as
\(x^2 + 4x + 4+5=(x+2)^2+5\)
Since x+2 is divisible by 10, hence
Rem(\(\frac{(x+2)^2+5}{10}\))=Rem(\(\frac{(x+2)^2}{10}\))+Rem(\(\frac{5}{10}\))=0+5=5

Ans. (C)
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If x is a positive integer and x + 2 is divisible by 10, what is the  [#permalink]

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New post 22 Aug 2018, 04:03
Bunuel wrote:
If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x^2 + 4x + 9 is divided by 10?

A. 1
B. 3
C. 5
D. 7
E. 9



x + 2 is divisible by 10. So, x + 2 is a multiple of 10.

thus x could be 8, 18, 28, 38, 48 and so on.


plug one of the value for x.

\(8^2 = 64\)
4*8 = 32

and 9.

64 + 32 + 9 = 105

105 / 10 = 10*10 + 5 .

So remainder is 5.

Thus the best answer is C.
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