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???
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Consecutive multiples
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mshaitianwhoa
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The Iceman
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Basically you have done calculation mistake. As per your formula the calculation should have been{(96-12)/4} + 1 =22mshaitianwhoa wrote: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???
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
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Brent@GMATPrepNow
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If you'd rather not memorize formulas, you can also try listing and looking for a pattern.mshaitianwhoa wrote:How many multiples of 4 are there between 12 and 96 inclusive?
My first inclination is to use the formula (Last-First)/Increment+1
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
Brent Hanneson - Creator of GMATPrepNow.com
