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gmatbusters
You are doing great man. These nuances will surely help you to avoid traps and to improve the score above 700. Maybe these kind of things make this forum unique from other GMAT forums. If I come across such concepts, then I will keep posting on this thread.
+1 to you
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Absolute Value function:

Concept 1)
|x-a|=b, it means distance of x from a = b
Attachment:
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download.png [ 7.1 KiB | Viewed 5928 times ]

Ques: Which equation gives the values of all numbers seven units away from 43?

A. |x + 7| = 43
B. |x – 7| = 43
C. |x – 43| = 14
D. |x – 43| = 7
E. |x + 43| = 7

Solution:
by definition of absolute value function.
|x – a| = b gives set of points x which are at a distance of b unit from a.
Hence |x – 43| = 7 gives all value of x at a distance of 7 from 43.

Answer D
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Concept2:
it can be logically deducted that , if |x-a|=|y-a|, it means either x= y or the x and y are equidistant from a, hence average of x & y = a , or x+y = 2a
Attachment:
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1)Sample Question:

|x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2

Solution:
|x+2|=|y+2|, it means either x and y are equal or are equidistant from -2.

(1) xy<0
it means one is positive and one is negative, hence they are not equal. so x and y are equidistant from -2, hence sum of x and y = -4. SUFFICIENT.

(2) x>2 y<2
x not equal to y, hence their sum is -4. SUFFICIENT.

Hence Answer D
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Hi gmatbusters, thank you for this thread. I came across your second post (a day ago, I guess) being mentioned by you in an answer, and was hoping you'd start a thread! :-) Here it is! Appreciate it :-)
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"The sum of the lengths of the shortest three sides of a quadrilateral must be longer than the longest side."

Construct a random quadrilateral ABCD.
Attachment:
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Join any two vertices(Say AC)

Now from triangle inequality j+k>n
Also n+m>l

So, from the above two equations we have j+k+m > l

Hence,

The sum of the lengths of the shortest three sides of a quadrilateral must be longer than the longest side.


It is analogous to triangle inequality theorem, which states that sum of two sides of a triangle is greater than third side.

In fact in any polygon, the sum of lengths of other sides must be longer than the last side.

Question using this concept:given that the length of each sies of a
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Only triangle is the polygon where equal sides proves regular polygon.


"If all sides of a triangle are equal, triangle is equilateral with all angles equal. It is a regular polygon."

"For polygons (other than triangle), equality of sides doesn't make it a regular polygon."


For example in quadrilateral, all sides equal proves Quadrilateral to be rhombus, not square.
we need additional information to prove the same.

Question based on this logic In the figure above
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Approach to find whether an expression is EVEN or ODD



It is a 3 step process:

1. \(n^x\) has the same Even and Odd nature as a \(n\) itself so always ignore the power it doesn't matter whether power \(x\) = 2, 3, 100 or so no provided that x is a positive integer.
Always ignore/delete the exponent provided that exponent is a positive integer.

2. Ignore/delete the term which u know is an Even number.

3. if the coefficient of n is odd integer, just ignore the coefficient and write it as n only for simplicity, if the coefficient of n is Even, ignore/delete the complete term as it is Even


Example Question:

Which of the following expressions yields an even integer for any integer n?


A. \(n^2-10n+21\)

B. \(n^2-2n-24\)

C. \(n^2+8n+7\)

D. \(n^2+11n+18\)

E. \(n^2-4n-60\)

discussed here:https://gmatclub.com/forum/which-of-the-following-expressions-yields-an-even-integer-for-any-inte-311785.html#p2416425
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