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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

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Re: 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

by Jay@ManhattanReview » Mon Jun 08, 2020 10:07 pm
BTGModeratorVI wrote: ↑
Mon Jun 08, 2020 11:54 am
 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

Answer: C
Source: Magoosh
Given that x + 2 is divisible by 10, say x = 8. Thus, x^2 + 4x + 9 = 8^2 + 4*8 + 9 = 64 + 32 + 9 = 105

So, 105 divided by 10 has a remainder 5.

The correct answer: C

Hope this helps!

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Re: 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

by Brent@GMATPrepNow » Sat Jun 13, 2020 5:13 am
BTGModeratorVI wrote: ↑
Mon Jun 08, 2020 11:54 am
 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

Answer: C
Source: Magoosh
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

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Brent
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Re: 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

by Scott@TargetTestPrep » Wed Jun 17, 2020 3:28 am
BTGModeratorVI wrote: ↑
Mon Jun 08, 2020 11:54 am
 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

Answer: C
Source: Magoosh
Solution:

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.

Answer: C

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Re: 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

by gentvenus » Wed Jun 17, 2020 10:55 am
C

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 w is 5.
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