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Problem solving OG 12. Experts please help me understand

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by arpan307 » Thu Jun 23, 2011 5:31 am
If 4< (7-x)/3, which of the following must be true?

I. 5<x
II. |x+3| > 2
III. -(x+5) is positive


Options :
(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III


The OA is D. I didn't get how to evaluate II condition. Experts kindly help on modulus.
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by Frankenstein » Thu Jun 23, 2011 5:48 am
Hi,
if |y| < a then -a < y < a
if |y| > a then y < -a or y > a where a is a positive number
So, here is how we evaluate II
|x+3| > 2.
So, x+3 < -2 or x+3 > 2
So, x < -5 or x > -1
Cheers!

Things are not what they appear to be... nor are they otherwise
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by Bens4vcobra » Thu Jun 23, 2011 6:05 am
Frankenstein wrote:Hi,
if |y| < a then -a < y < a
if |y| > a then y < -a or y > a where a is a positive number
So, here is how we evaluate II
|x+3| > 2.
So, x+3 < -2 or x+3 > 2
So, x < -5 or x > -1
I understand II but I can't see how III must be true. Could you demonstrate?

If x < -5 from the given expression, then how is it that -(x+5)'must be positive?'
"It takes no ability to give effort. Toughness is not God-given; it's a choice. The discipline to execute is a habit." - Nick Saban
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by Frankenstein » Thu Jun 23, 2011 6:10 am
Bens4vcobra wrote: If x < -5 from the given expression, then how is it that -(x+5)'must be positive?'
Hi,
As you have reached to x < -5, I will continue from this
x < -5. So, x+5 < 0 right?
So, (x+5) is negative implies -(x+5) is positive.
Cheers!

Things are not what they appear to be... nor are they otherwise
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by Bens4vcobra » Thu Jun 23, 2011 6:13 am
Frankenstein wrote:
Bens4vcobra wrote: If x < -5 from the given expression, then how is it that -(x+5)'must be positive?'
Hi,
As you have reached to x < -5, I will continue from this
x < -5. So, x+5 < 0 right?
So, (x+5) is negative implies -(x+5) is positive.
Thanks very much. I just figured out my error before I read your post. I had a "duh" moment. It was right in front of my face.
"It takes no ability to give effort. Toughness is not God-given; it's a choice. The discipline to execute is a habit." - Nick Saban
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by Ozlemg » Thu Jun 23, 2011 12:32 pm
Thank you. Great explanation...
The more you suffer before the test, the less you will do so in the test! :)
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