# Find three consecutive positive even integers whose sum is 90.

(a) 28, 30 and 32

(b) 28, 30 and 37

(c) 28, 98 and 32

(d) 40, 30 and 32

Answer

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Hint: Even integers are integers which are divisible by 2. For example: -2, -4, -6, 0, 2, 4, 6. The form of even integers are 2n, 2n+2, 2n+4 and so on. These are divisible by 2.

Complete step-by-step answer:

First of all we should know about integers. Integers are numbers that can be written without fraction. Set of integers is denoted by ‘Z’ or ‘I’. Integers can also be defined as, whole numbers together with negative of natural numbers comprise the set of integers. Positive integers are natural numbers like 1, 2, 3, 4….. . Now we should understand the term ‘consecutive’. Consecutive numbers means any selected number and its succeeding number. Example: two consecutive integers can be 1 and 2.

Now we have to select two consecutive positive even integers.

Let us consider one positive even integer as ‘2n’. Then ‘2n+1’ is its succeeding integer but it is not even as we can see it is not divisible by 2. Therefore consider ‘2n+2’, this integer is divisible by 2, therefore the next integer we have to select is ‘2n+2’. Now the next integer will be ‘2n+4’.

Now, coming back to question:

We have been given that the sum of 2n, 2n+2, 2n+4 is 90.

$\begin{align}

& \therefore 2n+(2n+2)+(2n+4)=90 \\

& \therefore 6n+6=90 \\

& \therefore 6n=84 \\

& \therefore n=14 \\

\end{align}$

Putting the value of ‘n’ in all integers, we get required integers,

\[\begin{align}

& 2n=2\times 14=28 \\

& 2n+2=28+2=30 \\

& 2n+4=28+4=32 \\

\end{align}\]

Hence option (a) is the correct answer.

Note: The concept of integers and even numbers should be clear. If we are in any competitive exam and time is less, then we can directly check it by the options given.

Complete step-by-step answer:

First of all we should know about integers. Integers are numbers that can be written without fraction. Set of integers is denoted by ‘Z’ or ‘I’. Integers can also be defined as, whole numbers together with negative of natural numbers comprise the set of integers. Positive integers are natural numbers like 1, 2, 3, 4….. . Now we should understand the term ‘consecutive’. Consecutive numbers means any selected number and its succeeding number. Example: two consecutive integers can be 1 and 2.

Now we have to select two consecutive positive even integers.

Let us consider one positive even integer as ‘2n’. Then ‘2n+1’ is its succeeding integer but it is not even as we can see it is not divisible by 2. Therefore consider ‘2n+2’, this integer is divisible by 2, therefore the next integer we have to select is ‘2n+2’. Now the next integer will be ‘2n+4’.

Now, coming back to question:

We have been given that the sum of 2n, 2n+2, 2n+4 is 90.

$\begin{align}

& \therefore 2n+(2n+2)+(2n+4)=90 \\

& \therefore 6n+6=90 \\

& \therefore 6n=84 \\

& \therefore n=14 \\

\end{align}$

Putting the value of ‘n’ in all integers, we get required integers,

\[\begin{align}

& 2n=2\times 14=28 \\

& 2n+2=28+2=30 \\

& 2n+4=28+4=32 \\

\end{align}\]

Hence option (a) is the correct answer.

Note: The concept of integers and even numbers should be clear. If we are in any competitive exam and time is less, then we can directly check it by the options given.

Last updated date: 29th Sep 2023

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