What is the amount of all of the four-digit integers that have the right to be created with the digits 1, 2, 3, and also 4?


Explanation:

First we require to discover out just how many possible numbers there are. The variety of possible four-digit numbers with four different digits is simply 4 * 4 * 4 * 4 = 256.

To uncover the sum, the formula we should remember is amount = median * number of values. The last item that"s lacking in this formula is the average. To find this, we have the right to average the first and last number, since the numbers space consecutive. The the smallest number that can be created from 1, 2, 3, and also 4 is 1111, and the biggest number feasible is 4444. Climate the median is (1111 + 4444)/2.

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So sum = 5555/2 * 256 = 711,040.


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Example concern #1 : consecutive Integers


Quantity A: The sum of all integers indigenous 49 come 98 inclusive.

Quantity B: The sum of all integers indigenous 51 to 99 inclusive.


Possible Answers:

Quantity A is greater.


Quantity B is greater.


The relationship cannot be figured out from the info given.


The two quantities are equal.


Correct answer:

The two amounts are equal.


Explanation:

For each quantity, only count the integers that aren"t in the various other quantity. Both quantities include the number 51 come 98, so those numbers won"t affect which is greater. Just Quantity A has actually 49 and 50 (for a full of 99) and only quantity B has 99. Since the excluded number from both quantities equal 99, you deserve to conclude the the 2 amounts are equal.


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Example inquiry #3 : continually Integers


What is the amount of all the integers between 1 and also 69, inclusive?


Possible Answers:

*


*


*



*


Correct answer:


Explanation:

The formula here is sum = mean value * variety of values. Due to the fact that this is a consecutive series, the average have the right to be found by averaging just the an initial and last terms: (1 + 69)/2 = 35.

sum = average * variety of values = 35 * 69 = 2415


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Example inquiry #4 : continually Integers


Quantity A: The amount of all integers native 1 come 30

Quantity B: 465


Possible Answers:

The partnership cannot be figured out from the info given.


Quantity B is greater.


The two amounts are equal.


Quantity A is greater.


Correct answer:

The two amounts are equal.


Explanation:

The amount of every integers native 1 come 30 have the right to be uncovered using the formula

*
, where 
*
is 30. In this case, the sum equals 465.


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Example inquiry #5 : continuous Integers


The sum of a set of 

*
 consecutive odd integers is
*
. What is the fourth number in this set?


Possible Answers:
Correct answer:

*


Explanation:

We have the right to represent our number as:

*

*
 will have to be one odd number since the whole sequence is odd. However, this will job-related out when we perform the math. Now, we understand that all of these included up will be 
*
. Us have 
*
 and the sum of the set 
*
, the amount of which is 
*
.

Thus, us know:

*

Solve for 

*
:

*

*

Therefore, the fourth facet will be 

*
:

*


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Example inquiry #6 : continually Integers


The typical of 5 consecutive integers is 

*
. What is the biggest of this integers?


Possible Answers:
Correct answer:

*


Explanation:

There are two ways to figure out this list of integers. ~ above the one hand, you can know the the mean of a set of continually integers is the "middle value" of that set. So, if the median is 

*
 and the size 
*
, the list need to be:

*

Another method to number this out is to stand for your integers as:

*

The typical of these values will be all of these numbers added together and then separated by 

*
. This offers us:

*

Multiply both political parties by 

*
:

*

Finish solving:

*

*

This means that the largest value is:

*


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Example question #7 : continually Integers


If the sum of 4 consecutive numbers is 38, what is the average of the largest and the the smallest of the 4 numbers?


Possible Answers:

8.75


9.5


10.5


11


11.75


Correct answer:

9.5


Explanation:

The amount of 4 consecutive numbers being 38 can be written as the following equation.

*

We have the right to simplify this to settle for x.

*

*

*

This tells us that the the smallest number is 8 and also the largest is (8 + 3) = 11. Native this, us can discover their mean.

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*


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