Question

any ten even numbers between 5000 and 6000​

Answer 1

Answer:

5002,5006,5008,5012,5014,5016,5022,5026,5028,5032

Answer 2

5008, 5320, 5744, 5550, 5896, 5378, 5122, 5510, 5142, 5100.

• Even numbers are defined as the numbers that are divisible by the single digit prime number 2.
• This means that these even numbers, when divided by 2 should give no remainder or give the remainder as zero which means that the number is entirely divided by 2.
• This also means number is divided exactly into two equal portions without any remainders.
• The numbers that satisfy the divisibility rule of the number two are called as even numbers.
• The set of whole numbers can be classified into two groups namely odd numbers and even numbers and the even numbers are the ones that are multiples of 2.
• The set of even numbers are: 2, 4, 6, 8, ......, 2n
• Thus, all the multiples of 2 come under the category of even numbers.
• The question asks to list out any 10 even numbers between 5000 and 6000 which means that the numbers 5000 and 6000 are not to be included in the list even-though they are even numbers .
• Since, all the whole numbers are divided into only 2 groups either odd or even; the numbers can either be even or odd which means that every alternate number starting from 2 is an even number.
• Half of the set of whole numbers out of the total lot are even.
• Thus, in-order to find out how many numbers are present between 5000 and 6000 we can take their difference.
• $\implies 6000-5000=1000 \; numbers$
• There are 1000 numbers present between 5000 and 6000 out of which half of them would be even.

Number of even numbers between 5000 and 6000= $\frac{1000}{2} =500$

• The total number of even numbers present between 5000 and 6000 is 500 out of which any ten is asked to be listed.
• So when we list out randomly we have:

5008, 5320, 5744, 5550, 5896, 5378, 5122, 5510, 5142, 5100.

• Here, it can be noted that each of these numbers end with an even number themselves and are divisible by 2 with 0 as remainder.
• The above is a random set of 10 even numbers between the interval 5000 and 6000.

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