Is it necessary to check absolute value solutions?

Question

For AV questions in general, is it necessary to plug in the positive case and negative case solutions back into the equation to make sure it doesn't produce a negative solution? In other words, is this something the GMAT tests?

Example question: https://gmatclub.com/forum/what-is-x-1- ... 26874.html

Want to make sure I'm not cutting corners for the sake of timing - thanks!

KarishmaB · Answer

No, you don't need to put it back and check but you need to understand the constraints under which you are getting the solution. |x| = 3x – 2 If x >= 0, then |x| = x So we get x = 3x - 2 x = 1 Since 1 is >= 0, this is a valid solution. If x < 0, then |x| = -x We get -x = 3x - 2 x = 1/2 Since x is not < 0, this is not a valid solution. Our initial condition must be met. Check: https://anaprep.com/algebra-the-why-beh ... questions/

achloes · Answer

KarishmaB  thanks - I'm clear on the issue. However, I do have a follow up question on this bit:

I can see why x could be a negative value. But why can't x be 0? Anything, including a negative value, multiplied by 0 is 0.

EMPOWERgmatRichC · Answer

Hi achloes, In the included prompt, we're told that X must be LESS than 0. To go back to your immediate question/concern, certain GMAT questions (and especially DS questions) are designed to 'test' your attention-to-detail and the thoroughness of your thinking. This does not necessarily mean that any 'math' involved will be difficult, but if you're prone to missing details or making little mistakes, then the GMAT is pretty good at catching you on that (and adjusting your Score accordingly). IF you did face an Absolute Value question in which you felt that you might need to 'check' your answers, then how long would it actually take you to do so? Would spending a couple of extra seconds just to make sure that you had the correct answer be worth it? (hint: I hope that you're leaning heavily towards "Yes"). GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com

KarishmaB · Answer

No, you don't need to put it back and check but you need to understand the constraints under which you are getting the solution. |x| = 3x – 2 If x >= 0, then |x| = x So we get x = 3x - 2 x = 1 Since 1 is >= 0, this is a valid solution. If x < 0, then |x| = -x We get -x = 3x - 2 x = 1/2 Since x is not < 0, this is not a valid solution. Our initial condition must be met. Check: https://anaprep.com/algebra-the-why-beh ... questions/

Is it necessary to check absolute value solutions?

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Is it necessary to check absolute value solutions?

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