What is the value of the greatest of these integers?
Statement 1: The integers are consecutive odd numbers.
Odd consecutive integers are odd integers that follow each other and they always have a difference of 2 between every two numbers.
Therefore, let n = lowest odd integer
4 consecutive odd integer = n, (n+2), (n+4), (n+6)
Greatest odd integer = (n+6)
Finding the value of n:-
n + (n+2) + (n+4) + (n+6) = 64
4n + 12 = 64
4n = 52
n = 13
Substituting the value of 'n' in 'n+6'
Greatest integer = n+6 = 13+6 = 19
Statement 1 is SUFFICIENT.
Statement 2: Of these integers, the greatest is 6 more than the least.
Let the four od integers = w, x, y and z
Let w=smallest integer and z=greatest integer.
Therefore, z=w+6
So, we have 4 odd integers =>
w < x < y < w+6 or w < y < x < w+6
Irrespective of whether they are consecutive or not, the only possible old number between w and w+6 is w+2 and w+6. So, the 4 odd integers will be w, w+2, w+4, and w+6. This is the same as the scenario in statement 1, so w = 13 and w+6=19. Hence, statement 2 is also SUFFICIENT.
Now that each statement alone is sufficient, the correct answer is option D.
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