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

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,

.

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

because if we don"t, we finish up no counting either the first or last page of the selection.