Source: Official Guide Revised GRE 1st Ed. Part 8; Section 6; #5

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# Three consecutive integers have a sum of -84

Three consecutive integers have a sum of -84. Quantity A : The least of the three integers Quantity B : -28 Quantity A is greater., Quantity B is greater., The two quantities are equal., The relationship cannot be determined from the information given.

### 1 Explanation

2 Chris Lele, Magoosh Tutor

Oct 11, 2012 • Comment

Nicholas Gregg Farmer

Hi! On this problem, I know the three digits would equal 90 if you did it this way, but why can't we subtract 1 instead of adding when setting up the initial algebra? Or if we can, why did you choose to add one first? So instead of what is in the answer it would start as [x+(x-1)+(x-2)]=-84

Hey Nicholas!
Remember that we want to find the smallest of these consecutive integers. The video uses x as the smallest integer, and x + 2 as the largest. This way, we can simply solve for x and find the smallest integer.

If we use x, x - 1, x - 2, then x is our greatest integer, and x - 2 is our smallest. So we have to solve for x first, and then subtract 2 from it to find the value of quantity A. Following the algebra, we should get x = -27, which means that our smallest integer, x - 2, will once again be -29. So you can do it this way, it just takes an extra step.
Hope that helps!