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If m is an even integer, then which of the following is the sum of the ... ...

If m is an even integer, then which of the following is the sum of the next two even integers greater than 4m + 1?


(A)

8m + 2


(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Math - Problem Set A: Substitution

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Posted: 01/24/2012 19:38
When I substitute in it seemed like e was the correct answer since allure others didn't work
Contributor
 
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Posted: 01/25/2012 01:56
Jr,

Substitute m for an even integer
m = 2
The question requires the answer to 4m + 1 first, ergo 'is greater than 4m + 1'
4 * 2 + 1 = 9
Now we need the next two even integers which are 10 and 12
The sum of the next two even integers is 10 + 12 = 22
We can see that all the first bits of every answer is 8m that make
8m + n = 22
8 * 2 + n = 22
16 + n = 22
Subtract 16 from both sides
n = 6
So we'll get
8m + 6 and that make C the correct answer

To verify we take m = 4
4m + 1 = 4 * 4 + 1 = 17
17 -> 18 + 20 = 38
8m + 6 = 38
32 + 6 = 38
38 = 38

Niels
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