Math Question?

[jay47]

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If N is any positive integer, how many consecutive integers following N are needed to ensure that at least one of the integers is divisible by another positive integer m?

A. m-1
B. m
C. m+1
D. 2m
E. m^2

Answer below:












Explanation says A, but I don't get it. Concept seems simple enough, but.... For example, let's say N is 10 ( a positive integer) and to make sure it is divisible by positive integer m= 2, it needs to be at least 8 or 12, therefore 2 integers following N, which would lead me to believe the answer is m+2. Not getting this one.

 

[Streetwolf]

If N is any positive integer, how many consecutive integers following N are needed to ensure that at least one of the integers is divisible by another positive integer m?

A. m-1
B. m
C. m+1
D. 2m
E. m^2

Answer below:












Explanation says A, but I don't get it. Concept seems simple enough, but.... For example, let's say N is 10 ( a positive integer) and to make sure it is divisible by positive integer m= 2, it needs to be at least 8 or 12, therefore 2 integers following N, which would lead me to believe the answer is m+2. Not getting this one.

Do a search cause I've answered this before quite extensively.

In short, two things.

1. It asks how many integers in terms of 'm' which is the number you are dividing by. So when you say m+2 (because 10+2 = 12), you really mean just 'm' because 10 + m = 10 + 2 = 12.

2. On that note, 10 itself is divisible by 2 so you wouldn't need to jump up to another integer. Now if you had 28 and you were trying to divide by 9, you'd need to go up 8 numbers (m - 1) to guarantee that you get something divisible by 9. Whenever you use m = 9, you need to select a series of 8 consecutive numbers to guarantee that one of them divides by 9 because the number you start with might be one above a number divisible by 9 (for example: 19, 28, 37, 46, etc - in all of those cases, you'd need to add 8 to get to the next number divisible by 9).

 

[jay47]

Do a search cause I've answered this before quite extensively.

In short, two things.

1. It asks how many integers in terms of 'm' which is the number you are dividing by. So when you say m+2 (because 10+2 = 12), you really mean just 'm' because 10 + m = 10 + 2 = 12.

2. On that note, 10 itself is divisible by 2 so you wouldn't need to jump up to another integer. Now if you had 28 and you were trying to divide by 9, you'd need to go up 8 numbers (m - 1) to guarantee that you get something divisible by 9. Whenever you use m = 9, you need to select a series of 8 consecutive numbers to guarantee that one of them divides by 9 because the number you start with might be one above a number divisible by 9 (for example: 19, 28, 37, 46, etc - in all of those cases, you'd need to add 8 to get to the next number divisible by 9).

I got it! My whole premise was based on the fact that the number N was already divisible by m, in which case you don't need to add or subtract anything. However, let's use eleven, in which case you would either need to add m-1 (which is 1) to get to 12 which is divisible by 12.