Given that the sum of five consecutive integers is 35 and we need to find the Value of the greatest integer to answer the problem

Let's solve the problem using two methods

Method 1: Algebra

Let first integer is n
=> next integer will be n+1, n+2, n+3, n+4

=> Sum of these five integers = n + n+1 + n+2 + n+3 + n+4 = 5n + 10 = 35 (given)
=> 5n = 35-10 = 25
=> n = \(\frac{25}{5}\) = 5

=> Value of the greatest integer = n + 4 = 5 + 4 = 9

=> Quantity A (Greatest Integer = 9) = Quantity B (9)

So, Answer will be C

Method 2: Formula (Arithmetic Series)

Since the integers are consecutive => it is an Arithmetic series or Arithmetic Sequence
And we know that for Arithmetic Series, Mean = Median = Middle Term
=> 3rd term which is middle term = Mean = \(\frac{Sum}{5}\) = \(\frac{35}{5}\) = 7

=> Greatest Integer will be 5th term = 3rd term + 2 = 9

=> Quantity A (Greatest Integer = 9) = Quantity B (9)

So, Answer will be C
Hope it helps!

Watch the following video to learn How to Sequence problems


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