GMATBuster's Error log/ Study Notes

Question

Hi Guys

GMAT is standardized test which is quite different from exams taken at school/undergraduate level.
It requires a lot of efforts to ace the test. In fact we need to act smartly, Regularity in studies is the basic key to success.
What I feel the  most important   strategy is to make error logs to remember what the mistakes committed earlier.
In fact trust me, If one can avoids the mistakes committed during the preparation in the real GMAT, one can easily get 700+.
Now onward, Whenever I come across any good concepts/ traps , I will post it here. this will serve as a error logs for me and for other GMAT aspirants.
you are also welcome to post your  selected concepts/error/traps here.

(PS: It is not the exhaustive study notes/theory, but only errors/new concepts encountered)

GMATBusters · Answer

Key concept:  In any Trapezium, the area of opposite triangles formed by intersection of diagonals and non parallel side are equal. 
but the other 2 triangles with parallel sides are NOT equal, they would be equal in case of Parallelogram.

Question based on this concept:  What is the area of triangle EBC?

(PS: Please note that the question can be done without this concept also, but sometimes we fall in traps/take longer time to solve. So, I personally like making and using these key concept)

GMATBusters · Answer

This is a simple concept, but the question framed on these are generally tricky:

1) If \(a^2+b^2 =c^2\), it means the angle between a & b is 90 deg, hence the triangle is right.
2) If \(a^2+b^2 < c^2\), it means the angle between side a & b is obtuse, the triangle is obtuse.
3) If \(a^2+b^2 > c^2\), it means the angle between a & b is acute, but since other angle can be obtuse, the triangle cant be taken as acute.

Attachment:

How to decide Acute or obtuse angle in a triangle.jpg [ 129.75 KiB | Viewed 8273 times ]

Out of above three, third property is MOST IMPORTANT.
Please note that If \(a^2+b^2 > c^2\), it simply tells that angle between a and b is acute, it doesn't mean that the triangle is Acute angled triangle.

Example of Questions based on this concept:
1)Is triangle ABC with sides a, b and c acute angled?
2)Is triangle ABC obtuse angled?

itisSheldon · Answer

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

GMATBusters · Answer

Absolute Value function:

Concept 1)
|x-a|=b, it means distance of x from a = b

Attachment:

download.png [ 7.1 KiB | Viewed 5667 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

GMATBusters · Answer

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:

WhatsApp Image 2018-04-17 at 22.17.07.jpeg [ 90.98 KiB | Viewed 5716 times ]

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

Wildflower · Answer

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

GMATBusters · Answer

"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:

gmatbusters2.jpg [ 12.4 KiB | Viewed 5417 times ]

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

GMATBusters · Answer

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

GMATBusters · Answer

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

bumpbot · Answer

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