SAT Math help » Arithmetic » Integers » counting » just how to uncover the variety of integers between two other integers

A custom-made leader is 

*
long and for every 
*
there"s a tick mark. How plenty of tick marks are there on the ruler?


*


*


*


*


*


Explanation:

There will be 15 gaps of 

*
long however 16 mite marks because there will certainly be a tick mark on each end of the ruler.

You are watching: How many integers are between 17 and 27


Explanation:

Let x equal the the smallest of the 4 numbers. Therefore:

*

*

*

*

Therefore the four odd numbers are 7, 9, 11, and 13. Since all space prime except 9, 3 of the numbers are prime.


The positive integer

*
 is not divisible by
*
. The remainder when 
*
 is split by
*
 and the remainder when
*
 is separated by
*
 are both equal to
*
. What is
*


Explanation:

We recognize that the remainder,

*
, need to be much less than
*
 by the an interpretation of remainder. Because of this our only selections are
*
,
*
, or
*
. We can test each of these cases. 

If

*
 would it is in divisible by
*
, i m sorry we claimed is no true. 

If

*
: try
*
. Then 
*
. As soon as we divide
*
 by
*
, we have actually a remainder that
*
. This works! 

If

*
: try
*
. Then 
*
. Once we division this by 
*
, we have actually a remainder of
*
. Thus, ours remainders room not equal. 

 

Thus,

*


Explanation:

Let"s look in ~ a little example, the numbers in between 1 and also 3 consisting of all endpoints. We have actually 1, 2, and also 3. If we subtract our numbers, we gain 2. We require to add one more to gain all the preferred numbers. We deserve to follow the same process with our bigger numbers. 

 

Take,

 

*
.

Then, including 1,

*
.

Therefore, our answer is 

*


Mrs. Lovell assigns she reading class to review pages three through sixty-four of your textbook. How many pages must each college student read? 


Explanation:

To counting the variety of pages in in between these two web page numbers, we want to subtract 

*
 and then add 
*
. We have to add 
*
 because if we don"t, we finish up no counting either the first or last page of the selection. 

Therefore, ours answer is 

*


Explanation:

An important consideration whenever you"re asked because that the variety of integers in between two various other numbers is to determine whether the two "end points" room included. Right here the indigenous "inclusive" tells united state that we need to count both -8 and 17 in our calculation.

A advantageous tip for these questions: if you"re including both finish points, you have the right to calculate by using the variety (greatest worth minus smallest value) and adding 1 come account for the inclusive set. (If you have to prove the to yourself, just use "how many integers between 1 and 3 inclusive" - clearly the set is 1, 2, 3 for three integers, yet 3-1 = 2, therefore you have the right to see you need to include one much more to acquire the answer).

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For this question, that pipeline us v 17 - (8) = 25 together the range, and if you include 1 to the for "inclusive" you obtain the exactly answer, 26.

Another method to look in ~ this one is to chop the up: between -8 and 17 there space 8 negative integers (-1 v -8), 17 positive integers (1 through 17), and 0 as one more integer. 8 + 17 + 1 = 26.