(I'm Overwhelmed) - Words to Algebra II Exercise Q7

GRE Quant Problem Solving
1

Hello,

I have a question regarding the solution to question #7 of the Words to Algebra II exercise’s, the question is below:

If three consecutive even integers have a product of 1,680 what is their sum?

In the solution, the answer key sets the problem up as:

x**(x+2)(x+4)=1680**

I understand that these are 3 consecutive integers, however I don’t understand how I’m meant to know to set up the solution in this from the start (setting it up as consecutive even integers). I set up the problem as:

(x-1)(x)(x+1) and then ran into the eventual issue of trying to solve x^3-x = 1,680

Any advice on what I’m missing or on recognizing the format of consecutive integers in this context (or generally) would be much appreciated!

Thanks

2

it’s easier to think about this if we play with easy numbers like 2, 4, and 6. Then you can see the error you made with (x-1)(x)(x+1) - that would be representative of consecutive integers, not consecutive even integers, which are separated by a distance of 2, not 1.