Manhattan 5lb - 100 Drills - Quant Question

GRE Quant Problem Solving
1

Quant problem: “For which values of a, if any , does |−6a+52|=−10a+76?”
Stated answer: a=6

Isn’t it also true that a=8 is one solution? Thanks

2

If you plug in a = 8, the left hand side becomes positive 4 while the right hand side remains negative 4.

3

Thanks for the quick reply and pointing that out, I see it now. What is the most common workflow for problems like these, defining the domain for the expression upfront, for example a must be greater than or equal to 7.6, or to plug back in each solution to determine which solutions are valid?

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4

I followed this after I solved for a

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5

One quick way to check if your value for a is correct or not is to see that the LHS value will always be postive due to the abs but the RHS value will only be positive for any negative value of a , zero and the positive values of a from 1 to 7{I am assuming integers as the ans choices are integers}.

6

Thank you!

7

Thank you, yes I see that. I hadn’t been training myself to look out for this kind of thing, but now I will be looking out for it. Thank you!