The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?

[BTGmoderatorDC]

The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?

(1) The integers are consecutive odd numbers
(2) Of these integers, the greatest is 6 more than the least.



OA D

Source: Official Guide

[deloitte247]

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.

Thanks

[Brent@GMATPrepNow]

The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?

(1) The integers are consecutive odd numbers
(2) Of these integers, the greatest is 6 more than the least.



OA D

Source: Official Guide

Target question: What is the value of the greatest of these integers?

Given: The 4 numbers are different odd integers, and their sum is 64.

Statement 1: The integers are consecutive odd numbers
Let x = the first odd integer
So, x + 2 = the 2nd odd integer
So, x + 4 = the 3rd odd integer
So, x + 6 = the 4th odd integer
Since we're told the sum is 64, we can write: x + (x+2) + (x+4) + (x+6) = 64
Since we COULD solve this equation for x, we COULD determine all 4 values, which means we COULD determine the value of the greatest of the 4 odd integers
Of course, we're not going to waste valuable time solving the equation, since our sole goal is to determine whether the statement provides sufficient information.
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Of these integers, the greatest is 6 more than the least.
Notice that the 4 CONSECUTIVE integers (from statement 1) can be written as x, x+2, x+4 and x+6
Notice that the biggest number (x+6) is 6 more than the smallest number (x).
Since the 4 odd integers are different, statement 2 is basically telling us that the 4 integers are CONSECUTIVE
So, for the same reason we found statement 1 to be SUFFICIENT, we can also conclude that statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent