Consecutive multiples

[mshaitianwhoa]

How many multiples of 4 are there between 12 and 96 inclusive?

My first inclination is to use the formula (Last-First)/Increment+1

This gave me 16.4 which was wrong. The book's answer is 22. Why did this formula not work???

[The Iceman]

How many multiples of 4 are there between 12 and 96 inclusive?

My first inclination is to use the formula (Last-First)/Increment+1

This gave me 16.4 which was wrong. The book's answer is 22. Why did this formula not work???

Basically you have done calculation mistake. As per your formula the calculation should have been{(96-12)/4} + 1 =22

As a general rule, basically you need to do this [N/k] - [M/k] if you need to find the number of multiples of k between M and N exclusive, where [x] denotes the greatest integer less than or equal to x. E.g. [2.4]=[2.7]=2, [-3.6]= -4, [3]=3

[96/4] - [12/4] + 1 = 22 (we added 1 because the problem mentions "inclusive")

For instance, if you were required to find number of multiples of 3 between 17 and 128, your answer would be [128/3] - [17/3] = 42-5 = 37

[Brent@GMATPrepNow]

How many multiples of 4 are there between 12 and 96 inclusive?

My first inclination is to use the formula (Last-First)/Increment+1

If you'd rather not memorize formulas, you can also try listing and looking for a pattern.
Let's list the multiples of 4 from 12 to 96 inclusive.

12 = 4(3)
16 = 4(4)
20 = 4(5)
24 = 4(6)
.
.
.
88 = 4(22)
92 = 4(23)
96 = 4(24)

As you can see, the number of multiples of 4 from 12 to 96 inclusive is equal to the number of integers from 3 to 24 inclusive.

Well, we know that the number from integers from x to y inclusive equals y - x + 1

So, the number of integers from 3 to 24 inclusive equals 24 - 3 + 1 = 22

Cheers,
Brent