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Inequalities Solutions (MGMAT Prep Question)

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by ostrowskiamy » Wed Feb 13, 2013 7:31 pm
Hi folks! Thanks SO much for the many answers I received to my previous post (I moved onto inequalities in the interim, but I'll loop back on those answers with some well-deserved "thank you's" and responses asap!

This one threw me:

"If (AB)/7 > (1/14) and A = B, which of the following must be greater than 1?

A) A+B
B) 1-A
C) 2A(^2)
D) A(^2)-(1/2)
E) A

The solution provided explains that:

14AB > 7 (cross multiply to get that)

2AB>1 (then, divide both sides by 7)

= 2A(^2) > 1, so the answer is C.

...Why divide by 7? I thought we would need to divide both sides by 14, to get the inequality alone??

Thank you in advance for any insights/tips!

Best,
Amy
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by Tommy Wallach » Wed Feb 13, 2013 7:38 pm
Hey Amy,

Basically, you want to divide by 7 because then you won't have any fractions. Isolating the AB is nice, but it's nicer to have all integers (also, having something greater than 1 is helpful, considering what the question was asking)! You could always do it the other way...

AB > 1/2

A^2 > 1/2

Then, you could look at the answer choices, and see that if you multiplied both sides of your current equation by 2, you'd end up with an answer choice:

2A^2 > 1

Hope that helps!

-t
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by ostrowskiamy » Wed Feb 13, 2013 7:42 pm
Thanks so much, T! So I CAN just divide 7 by...itself? Ha, I don't recall ever actively doing this! It just seems like a strange concept, to divide something by itself when nothing needs to be cancelled. If it's 'allowed' though..I'll run with it!
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by ostrowskiamy » Wed Feb 13, 2013 7:47 pm
...One more inequality question while I have you, if that's alright:

(x+1)(^2) < 36
sq.root of this is < 36
I x +1 I < 6
-7 < x < 5

I understand why I need to put the absolute value brackets in, during the third step...but I think that's mostly because I know I'm working with absolute values & just studied that section of the book! How can I remember to do that on test day? Should I ALWAYS do that when working with inequalities, where part of the solution (here, the variable) is in parentheses?

Thanks again! Your answers are extremely helpful and well-explained!

Best,
Amy
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by Tommy Wallach » Wed Feb 13, 2013 8:06 pm
Hey Amy,

Annoying as it may sound, could you post it in a separate thread, then PM me about it. We like to keep threads 1 question per...

-t
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by ostrowskiamy » Wed Feb 13, 2013 8:12 pm
Hey, I'm getting some awesome free help - it is NOT a problem at all! :)
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