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

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Joined: 02 Sep 2009
Posts: 56261
If x is a positive integer and x + 2 is divisible by 10, what is the  [#permalink]

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22 Aug 2018, 03:07
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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

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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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22 Aug 2018, 03:14
1
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

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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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22 Aug 2018, 03:15
3
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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22 Aug 2018, 05:03
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.
If x is a positive integer and x + 2 is divisible by 10, what is the   [#permalink] 22 Aug 2018, 05:03
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