SAT Math : How to find the number of integers between two other integers

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : How To Find The Number Of Integers Between Two Other Integers

A custom-made ruler is 30\ cm long and for every 2\ cm there's a tick mark. How many tick marks are there on the ruler?

Possible Answers:

14

18

16

17

15

Correct answer:

16

Explanation:

There will be 15 gaps of 2\ cm long but 16 tick marks because there will be a tick mark on each end of the ruler.

Example Question #2 : How To Find The Number Of Integers Between Two Other Integers

How many prime numbers are between 1 to 25?

Possible Answers:

Correct answer:

Explanation:

A prime numbers is a number greater than 1 that can only be divided by 1 and itself. Simply count from 1 to 25 and see how many values fit the criteria.

2, 3, 4, 5, 6, 78, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25

Prime numbers are bolded. Nine prime numbers are in this set interval.

Example Question #3 : How To Find The Number Of Integers Between Two Other Integers

Four consecutive odd integers sum to 40. How many of these numbers are prime?

Possible Answers:

Correct answer:

Explanation:

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

\dpi{100} x + (x+2)+(x+4)+(x+6)=40

\dpi{100} 4x +12 = 40

\dpi{100} 4x + 28

\dpi{100} x=7

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

Example Question #4 : How To Find The Number Of Integers Between Two Other Integers

The positive integer  is not divisible by . The remainder when  is divided by  and the remainder when  is divided by  are both equal to . What is

Possible Answers:

Correct answer:

Explanation:

We know that the remainder, , must be less than  by the definition of remainder. Therefore our only choices are , , or . We can test each of these cases. 

If   would be divisible by , which we said is not true. 

If : Try . Then . When we divide  by , we have a remainder of . This works! 

If : Try . Then . When we divide this by , we have a remainder of . Thus, our remainders are not equal. 

 

Thus,

Example Question #1713 : Sat Mathematics

How many integers lie between  and , including the end points? 

Possible Answers:

Correct answer:

Explanation:

Let's look at a small example, the numbers between 1 and 3 including all endpoints. We have 1, 2, and 3. If we subtract our numbers, we get 2. We need to add one more to get all the desired numbers. We can follow the same process with our larger numbers. 

 

Take,

 .

Then, adding 1,  

.

Therefore, our answer is 

Example Question #1714 : Sat Mathematics

How many integers are between  and

Possible Answers:

Correct answer:

Explanation:

In order to obtain the numbers between -8 and 17, you can draw a number line starting with -8 on the left, 0 in the middle, and 17 on the right. 

In order to get from -8 to 0, you must move 8 integers.

In order to get from 0 to 17, you must move 17 integers.

In total, you move  integers, which gives the final answer:  integers.

Example Question #1715 : Sat Mathematics

Mrs. Lovell assigns her reading class to read pages three through sixty-four of their textbook. How many pages must each student read? 

Possible Answers:

Correct answer:

Explanation:

To count the number of pages in between these two page numbers, we want to subtract  and then add . We have to add  because if we don't, we end up not counting either the first or last page of the selection. 

Therefore, our answer is 

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