Bunuel wrote:

marcusaurelius wrote:

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

21

22

23

24

25

My answer was 21 and that's incorrect.

\(# \ of \ multiples \ of \ x \ in \ the \ range = \frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1\).

In the original case: \(\frac{96-12}{4}+1=22\).

If the question were: how many multiples of 5 are there between -7 and 35, not inclusive?

Last multiple of 5

IN the range is 30;

First multiple of 5

IN the range is -5;

\(\frac{30-(-5)}{5}+1=8\).

OR:How many multiples of 7 are there between -28 and -1, not inclusive?

Last multiple of 7

IN the range is -7;

First multiple of 7

IN the range is -21;

\(\frac{-7-(-21)}{7}+1=3\).

Hope it helps.

I have one concern regarding this How many multiples and how many integers?

How many of the three-digit numbers are divisible by 7?

Generally we do--->999-100= 899

so 899/7=128 so we need to include both digits so we add 1 to total so it is 128+1

but the answer is only 128,How is that possible?????

As per our knowledge we know that

->If the question says both inclusive we add +1 at the last, For eg

How many of the three-digit numbers are divisible by 7?

Generally we do--->999-100= 899

so 899/7=128 so we need to include both digits so we add 1 to total so it is 128+1

->If the question says both not inclusive we add -1 at the last, For eg

How many of the three-digit numbers are divisible by 7?

Generally we do--->999-100= 899

so 899/7=128 so we need to include both digits so we add 1 to total so it is 128-1

->If the question says one inclusive we only subtract two extremes, for Eg

How many of the three-digit numbers are divisible by 7?

Generally we do--->999-100= 899

so 899/7=128, so 128 is the answer.....

Anything wrong with my concept???????Please explain i am totally confused with this...............

If anything wrong,please explain how to with these kind of problems, Like How many integers between two numbers? and How many integers between two multiples?

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