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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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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

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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, 02:14
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, 02:15
3
1
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, 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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If x is a positive integer and x + 2 is divisible by 10, what is the  [#permalink]

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09 Sep 2019, 07:14
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

Least value of x to be divisible by 10 is x = 8

Now, $$\frac{x^2 + 4x + 9}{10} = \frac{8^2 + 4*8 +9}{10}=\frac{105}{10}$$

Thus, Remainder will be 5, Answer must be (C)
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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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04 Feb 2020, 09:32
1
Top Contributor
Bunuel wrote:
If x is a positive integer and x + 2 is divisible by 10, what is the remainder when x² + 4x + 9 is divided by 10?

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

Given: x + 2 is divisible by 10
In other words x + 2 is a multiple of 10, which means we can write: x + 2 = 10k for some integer k

We want to know what the remainder will be when we divide x² + 4x + 9 by 10.

x² + 4x + 9 = x² + 4x + 4 + 5
= (x +2)(x +2) + 5
= (10k)(10k) + 5
= 100k² + 5
So now we want to know what the remainder will be when we divide 100k² + 5 by 10.

We can already see that 100k² [aka (10)(10k²)] is a MULTIPLE of 10
So, 100k² + 5 is 5 greater than a multiple of 10
So, the remainder will be 5 when we divide 100k² + 5 by 10

Cheers,
Brent
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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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08 Feb 2020, 19:18
1
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

Since x + 2 is divisible by 10, then x + 2 could equal 10, and hence, x could equal 8. (Note, that x + 2 could also equal 20, or 30, or any positive multiple of 10).

We’ll choose x = 8, and we have:

8^2 + 4(8) + 9 = 64 + 32 + 9 = 105

Since 105/10 = 10 R 5, the remainder is 5.

Alternate Solution:

Let’s write x^2 + 4x + 9 = x^2 + 4x + 4 + 5 = (x + 2)^2 + 5.

Since x + 2 is divisible by 10, (x + 2)^2 is also divisible by 10. Hence, the remainder when x^2 + 4x + 9 = (x + 2)^2 + 5 is divided by 10 is 5.

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Re: If x is a positive integer and x + 2 is divisible by 10, what is the   [#permalink] 08 Feb 2020, 19:18
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