# 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

Last updated date: 23rd Mar 2023

•

Total views: 306.6k

•

Views today: 3.85k

Answer

Verified

306.6k+ views

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.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India