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If x is a positive integer and x + 2 is divisible by 10, wha
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Updated on: 04 Feb 2020, 08:50
Updated on: 04 Feb 2020, 08:50
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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
A. 1
B. 3
C. 5
D. 7
E. 9
Re: If x is a positive integer and x + 2 is divisible by 10, wha
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04 Feb 2020, 08:19
04 Feb 2020, 08:19
1
If x is a positive integer and x + 2 is divisible by 10 then the values possible for x are 8,18,28,.....
Let's take x = 8.
\(x^{2} + 4x + 9 = 8^{2} + 4 \times 8 + 9 = 64 + 32 + 9 = 105\)
105 divided by 10 leaves a remainder of 5.
OA,C
Let's take x = 8.
\(x^{2} + 4x + 9 = 8^{2} + 4 \times 8 + 9 = 64 + 32 + 9 = 105\)
105 divided by 10 leaves a remainder of 5.
OA,C
huda 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
A. 1
B. 3
C. 5
D. 7
E. 9
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x is a positive integer and x + 2 is divisible by 10, wha
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04 Feb 2020, 09:33
04 Feb 2020, 09:33
huda 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
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
Answer: C
Cheers,
Brent
