Concept Of Factors

Concept of Factors:
N = P^a * Q^b * R^c (Where P,Q and R are prime numbers and a, b and c are natural numbers)
Then
1. Total no of factors of N = (a+1)*(b+1)*(c+1)
2. Total no of perfect square factors of N= (a+1)/2 * (b/2+1) *(c+1)/2 [If a and c is an odd no, b is an even no]
3. Total no of odd factors of N= (1 * (b+1)*(c+1)) [If P=2]
4. Total no of odd factors of N= (a+1)*(b+1)*(c+1) [If 2 is not the factor of N]
5. Total no of even factors of N= (a * (b+1)*(c+1)) [If P=2]
6. Total no of even factors of N= 0 [If 2 is not the factor of N]
7. Total no of non ordered pairs of (x,y) such that (x * y = N) = [(a+1)*(b+1)*(c+1)]/2 note : If total no of factors is an even no.
8. Total no of non ordered pairs of (x,y) such that (x * y = N) = [(a+1)*(b+1)*(c+1)+ 1]/2 note : If total no of factors is an odd no.
9. Total no of co-prime pairs using all the factors of N = a+b+c+2 (ab+bc+ca) + 4abc
10. Sum of all the factors of N = [(P^(a+1) – 1)/(p – 1)] * [(Q^(b+1) – 1)/(Q – 1)] * [(R^(c+1) – 1)/(R – 1)]

Common Errors

Hello People,
I am back to discuss certain inadvertant mistakes that we tend to commit while solving sentence correction questions. I chanced upon few of these on the internet and consider it worth to share with all of you. Fine nuances of grammar, here it goes...
Aspect Vs Respect:
These two words are widely used when talking about different perspectives of an idea but we have to keep in mind that they are NOT interchangeable, like we can say "in all/some/this RESPECT" but we cannot say "in all/some/this ASPECT". But we look at all ASPECTS of an issue and not RESPECTS of an issue.

As less as possible:
Now many of us are going to be surprised to know this...the expression is "as little as possible" and NOT "as less as possible".

As time progressed/passed:
Time as such can never progress...events progress...time passes.So the correct expression should be "as time passed".

Everyone/Every one:
“Everyone” means “everybody” and is used when you want to refer to all the people in a group: “Everyone in my family is an engineer.”
But while referring to the individuals who make up a group, then the phrase is “every one.” like “We wish each and every one of you a Merry Christmas” (every single one of you).

New lease of/on life:
Reinvigorated people are said to have been granted with a "new lease on life" and not "new lease of life."

For sale/On sale:
When you sell something it is "for sale" and when you lower the price it is "on sale".

Maybe/May be:
Maybe is an adverb meaning "perhaps", like "Maybe he is coming for the party" and this sentenece MAY BE rephrased by "Perhaps he is coming for the party"(Now you get the difference?)

Worse comes to worse/Worst comes to worst:
The traditional phrase was "worst comes to worst", however with the passage of time a more logical form has been adopted i.e. "worse comes to worst". The phrase "worse comes to worse" is simply incorrect.

Possessed of/by/with:
When you own any object or thing the you are "possessed of it"; You are "possessed by" a spirit; When you have a strong desire to win, you are "possessed with" passion for vistory and success.

AND

If Vs Whether:
While discussing two possibilities it is always advisable to use WHETHER and in case of conditional clauses, the use of IF is preferred. "I do not know whether you want to go for the movie" and "You must go for the film IF you want to meet him"

Phew...that was quite an exhaustive fact finding tour, wasn't it?? I shall surely keep all of you updated with many more errors of this kind. Till then let's continue our efforts of conquering the world of grammar!!!

Let’s start the preparation for CAT DI section:

Drill 1 :Become Comfortable with calculations:
You should have a good command on tables and Squares (up to 30).
Now we will check how to do approximate calculations
For example Dividing 283 by 1983 and finding that value as a percentage.
283/1983: whenever denominator is greater than numerator try to approximate denominator. Hence you could take 1983 as 2000.
So now our question looks like 283/2000 which is noting but 0.1415 or 14.15%. Here we change our denominator by 17 which is approximately 1% 0f 1983(19.83).
So in our answer also approximately 1% error is there. 1% of 14.15% is nothing but 0.14%. So our final answer has to be 14.15% + 0.14% = 14.29%.
Now we will check what to do if numerator is greater than denominator, for example Dividing 1132 by 1069.
1132/1069: Here we can write 1132 as 1069 + 63 which will leads to 1 + 63/1069.
So now if we do approximation, it is on very small part. 63/1069≈0.06 and our final answer is 1.06 or 106%.
I hope now the concept of approximation is clear. Just try to solve few questions:
412/6950 a) 5.9% b) 4.7% c) 5.2% d) 6.2% e) 5.72%
511/1680 a) 31.5% b) 29.3% c) 30.1% d) 32.2% e) 30.4%
6.4/6.12 a) 1.045 b) 1.053 c) 1.035 d) 1.023 e) 1.031.

MH-CET results out!

Check out your MH-CET results at dte.org.in/result.

Do keep posting your scores and category for any suggestions...Highest heard till now- 148 (equivalent to 99.92%ile). Will keep updating the highest scores...

All the best!

Stop and Think

Just came across this video a few days ago. It has definitely touched me and I wanted to share it with you. Hope it makes a small difference at least, and compels us to act differently. Well the video is called “value of 500 rs.”

Check the link out:
http://www.youtube.com/watch?v=M0XTPSYdP08

Challenger Logic Puzzle

Saturday, Kelly and four of her friends, lured by advertisements of the "biggest sale of the year," went Christmas shopping at Tracy's. Each of the five found the sales pitch to be true, finding a gift for her dad--one buying a sweater--at a great price. Given the clues below, can you solve this Challenger Logic Puzzle by determining the item each purchased, its original price, and its price on sale Saturday?
1 The original prices ranged from a low of $30 to a high of $120, totaling $310 for the five gifts.
2 The girls ended up spending $134 total on their five gifts, from a low of $21 to a high of $36,
3 The price of Jada's gift was reduced 20% more than the price of the tie, but Jada still paid $4 more for her item than the girl who bought the tie for her dad paid.
4 The original price of Lynne's gift was $50 more than the original price of the gloves another girl bought her dad, but after Tracy's reductions Lynne spent only $8 more than the gloves purchaser did.
5 Maria saved $7 more than the girl who bought the belt did.
6 The sale price of the dress shirt was $4 more than the sale price of the item Nicole purchased.
7 The biggest discount on any of the five items was 70% and the smallest discount was 30%.