on the same note.

If d is POSITIVE and |x| < d, then -d < x < d
If d is NEGATIVE and |x| < d, then there is no solution

If d is POSITIVE and |x| > d, then x < -d OR x > d
If d is NEGATIVE and |x| > d, then x is all real numbers

If x > y, then x - y divides x^n - y^n.

interesting....can someone provide a proof for this...thx

oh. I was wondering that we were able to post attachments for a while.. hmmm looks like its gone..

Hello Ywilfred,
I am not sure if "- x < 5 --> x>5" is the correct !
Since -X < 5 => X > -5.
I think for absolute value problems, we need to do as follows,

|x-4| < 9
1: In order to get rid of absolute value we need to consider + and -ve.
=> X-4 < 9 => X < 9 + 4 => X < 13 ----> (1)
and second,
=> X-4 > -9 => X > -5 ------> (2)
(note that when we take the -ve value we flip the operator)
Combining (1) and (2) we get
-5 < X < 13.
Kindly let me know if I am wrong....
Cheers,
Ravindra.

Hi vprabhala, I've promised to post something regarding basic sets and venn diagram principles here and so here it is, finally.

I've written a document explaining two concepts you can use to solve problems invovlving sets. In this document, I've taken out some examples posted on GMATClub quite some time ago and apply the concepts explained.

Hope this document is useful for members here.

As usual, if you spot any mistakes in my working, please let me know and I'll have them changed. Thanks.

(Note: I've converted my document to a PDF format so it takes up less space)

Glad it's of use !

sure thing folaa3. Give me some time to compile it, and i'll see if i can add in anything about rectangular coordinates too. By the way, what do you mean by advanced pointers ? The ones tested seem pretty fundamental.

Working with Ratios

Ratio questions are very easy to solve if you have mastered the way of thinking.

Basically if you have
a/b=c/d (or a:b=c:d)
then you can immediately derive a variaty of correlated ratios, such as:
a/(a+b)=c/(c+d)
a/(a-b)=c/(c-d)
(a+b)/(a-b)=(c+d)/(c-d)
(a+c)/(b+d)=c/d
(a-c)/(b-d)=c/d
etc

Basically, you can do all kinds of additions and subtractions.

Example:

a/b=3/5 (1)
2a-b=4 (2)
What is a?
From (1) we get a/(2a-b)=3/1, so a=3*4=12
Explanation: a is 3 share, b is 5 share. Two a is 6 share, 2a-b is one share. If one share is 4, then 3 share is 12.

Of course this question can be solved using the more traditional algebra approach:
b=5/3a
substitute in (2)
2a-5/3a=4
1/3a=4
a=12

You can see the two approaches are really the same in nature. However the first approach is very straight forward and does not involve calculation in fractions. Sometimes it can save you lots of time, especially when using this method with word problems such as mixture problems.

Mixture Problems

Example:

A fruit mixture is made up by 25% fruit A and 75% fruit B. Now if the amount of fruit A is doubled, what is their relative share in the new mixture?

A:B=25:75
2A:B=50:75=2:3
The new mixture total quantity is 2A+B
2A:(2A+B)=2:5
B:(2A+B)=3:5
Therefore the new shares are fruit A 40%, fruit B 60%.

Example 2:

In a picnic 60% people ate two hotdogs, 30% people ate one hamburger, and 10% people ate one hotdog. The total number of hotdog and hamburgers consumed is 80. How many hamburgers and hotdogs are consumed?

People:
T:H:O=6:3:1 (1)
Food:
2T+H+O=80
From (1)
T:H:O:(2T+H+O)=6:3:1:16
Therefore
T:(2T+H+O)=3:8=30:80 30 people ate two hotdogs
H:T=3:6=1:2=15:30 15 people ate one hamburger
O:T=1:6=5:30 5 people ate one hotdogs
Total people 50, total hotdogs 65, total hamburgers 15.
Verify, total hotdogs and hamburgers=65+15=80.

Just learned this today so thought i would add it here -

A simple test to find out if a number is divisible by 7 -

"Double the units and subtract from the tens. Keep going in the chain till you cannot get any further. If the end result is a zero or a multiple of 7 then the entire number is divisible by 7"

e.g - 1365 -> 136-(5*2) -> 126 -> 12-(6*2) -> 0. Hence 1365 is divisible by 7.

e.g - 1367 -> 136 - (2*7) -> 122 -> 12 - (4*2) -> 4. Hence 1367 is not divisible by 7.