Is √(y-4)^2 = 4-y

by **ShaneL361** Mon Sep 22, 2014 4:01 am

Is √(y-4)^2 = 4-y

1) |y-3| ≦ 4-y

2) y * |y| > 0

Hope it's ok to post this one in this forum. This problem is from the Algebra I handout so I'm not sure how representative it is of a GMAT problem but I'm a bit confused. If I could get a clearer answer it would be much appreciated.

Since this simplifies to |y-4| = 4-y, can we not break this down into the two equations (y-4) = 4-y, and (y-4) = -(4-y)? The answer only takes the one path of using |y-4| = -(y-4) and I'm not sure why that is.

Thanks,

Shane

by **RonPurewal** Mon Sep 22, 2014 2:05 pm

The left-hand side will sometimes be equivalent to (y – 4); at other times it will be equivalent to (4 – y).

The key is to figure out WHEN it simplifies to each of these. Don't just memorize random transformations. Understand how they work, and why.

Try investigating the expression √(y – 4)^2. Just plug in a bunch of numbers for y, and watch what happens. (hint: be sure to plug in values above 4 as well as values below 4.)
After you investigate for a bit, a pattern should appear.

by **ShaneL361** Tue Sep 23, 2014 3:03 am

Thanks Ron.

by **tim** Wed Sep 24, 2014 12:02 am

by **RonPurewal** Wed Sep 24, 2014 4:05 am

In particular, you should find that the answer to the question is "yes" for all y ≤ 4 (and only for those values).

Is √(y-4)^2 = 4-y

Is √(y-4)^2 = 4-y

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