Question

If the sum of four consecutive integers is 38, what is the value of second consecutive integer?
(a) 8
(b) 9
(c) 10
(d) 11

Answer 1

Hint: Let the smallest integer out of the four be x. We know that the consecutive integers differ by 1 from the previous one, so the rest of the three integers are (x+1), (x+2) and (x+3). As it is given that the sum of the four integers is 38, we will add the four integers and equate the result with 38 and solve the equation to get the answer.

Complete step-by-step answer:
First, let us try to recall the definition of integer.
So, the basic definition of integer is “all the rational numbers which can be written without the use of any fractional component no matter whether it’s positive or negative is termed as integers.”
Now let us start the solution to the above question by letting the smallest integer out of the four be x. We know that the consecutive integers differ by 1 from the previous one, so the rest of the three integers are (x+1), (x+2) and (x+3).
Now, as it is given that the sum of the four integers is 38, we will add the four integers and equate the result with 38. On doing so, we get
 $ x+\left( x+1 \right)+\left( x+2 \right)+\left( x+3 \right)=38 $
 $ \Rightarrow 4x+6=38 $
 $ \Rightarrow 4x=32 $
Now, we will divide both sides of the equation by 4. On doing so, we get
 $ x=\dfrac{32}{4} $
 $ \Rightarrow x=8 $
So, the integers x, (x+1), (x+2) and (x+3) are 8, 9, 10 and 11, respectively.
So, we can clearly see that the second consecutive integer is 9. Hence, we can conclude that So, the correct answer is “Option B”.

Note: See a mistake that a student can make is letting the consecutive integers be a, b, c and d and then taking the difference between the two consecutive integers to be 1. That might give you the answer but you have to solve for different equations and it is not necessary that you will be able to solve the system of 4 equations in the constraint of time. We can also solve by taking the second consecutive term as x, so the four terms will be (x-1), x, (x+1) and (x+2). Now, solving the equation, directly we get the value of x as the final answer.