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Papgust's GMAT MATH FLASHCARDS directory

Problem Solving — algebra and arithmetic
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by papgust » Sat Jun 12, 2010 7:36 pm
Another point to remember:

Example:

-1/10 < n < 1/10

After taking reciprocal of n, FLIP SIGNS!

-10 > n > 10
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by papgust » Sat Jun 12, 2010 7:40 pm
Example:

|x+y| < |x| + |y|


1. If x and y have SAME SIGNS, then both sides will be equal.

2. If x and y have DIFFERENT SIGNS, then right side will be greater.
Last edited by papgust on Tue Jun 15, 2010 8:44 pm, edited 1 time in total.
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by viju9162 » Sun Jun 13, 2010 6:07 am
Hi Papgust,

Wonderful tips!! Please keep posting.

Regards,
Viju
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by papgust » Sun Jun 13, 2010 5:44 pm
viju9162 wrote:Hi Papgust,

Wonderful tips!! Please keep posting.

Regards,
Viju
Thanks viju! :) Sure, I will. Nice to see you back after a long break.

---

That is the end of "INEQUALITIES". I will start posting on the chapter "AVERAGES".

Forthcoming points on "AVERAGES" are all very important takeaways. I'm sure that you will definitely benefit from these points.
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by papgust » Sun Jun 13, 2010 5:51 pm
Weighted Averages:

In weighted averages involving 2 groups, if you have any 3 of the following, you can ALWAYS FIND the fourth:

- Average of Group #1
- Average of Group #2
- Overall Average
- Ratio of Group #1 to Group #2

Solve this GMATPrep question to understand the trick!


NOTE: This takeaway is especially useful for Data Sufficiency questions for which you sometimes do not need to solve for the answer. When you see any 3 points in the question and statement and when you are asked to calculate the fourth point, you DON'T need to solve actually. You can straight away conclude that the statements are sufficient.


Courtesy: Ian Stewart, GMAT Expert.
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by papgust » Sun Jun 13, 2010 6:04 pm
A way to solve "Weighted Averages":


Avg Group 'A' ........... X ............ Overall Avg ............ Y .................... Avg Group 'B'

where, X is the distance b/w Group 'A' and Overall Avg and Y is the distance b/w Group 'B' and Overall Avg.


A/B = Y/X


Example:
A class writes a math test and the overall average is 75%. If the girls average 85% and the boys average 70%, what fraction of the class is boys?


Boys (70%) ............ 5 ............... Overall Avg (75%) ............. 10 ............... Girls (85%)

B/G = 10 / 5 = 2/1
B:G = 2:1

The class is 2/(2+1) OR 2/3 boys
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by sumanr84 » Mon Jun 14, 2010 3:10 am
I really appreciate your effort..Thanks a lot !!
I am following it everyday..;-)
I am on a break !!
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by papgust » Mon Jun 14, 2010 6:28 am
sumanr84 wrote:I really appreciate your effort..Thanks a lot !!
I am following it everyday..;-)
I'm flattered..! Thank you :)
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by papgust » Mon Jun 14, 2010 6:30 am
Standard Deviations:

In order to calculate Standard Deviations, you need the following data points,

- Population of the Data set [-- Total Number of elements in the set --]
- Mean of the Data set
- Data points/elements themselves

EXCEPTION:
If the set has CONSECUTIVE INTEGERS, you DO NOT need to know the Data points/elements.
But knowing NUMBER OF TERMS (or POPULATION) is must.


Courtesy: Ian Stewart, GMAT Expert.
Last edited by papgust on Mon Jun 14, 2010 6:42 am, edited 1 time in total.
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by papgust » Mon Jun 14, 2010 6:32 am
--[ IMPORTANT POINTS ]--


If a constant percentage is added/subtracted from each term of the set, then the new SD is also added/subtracted by that constant percentage.


If a constant is added/subtracted from each term of the set, then the new SD remains constant.
Last edited by papgust on Mon Jun 14, 2010 6:35 am, edited 1 time in total.
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by papgust » Mon Jun 14, 2010 6:34 am
If you add data that is farther from the mean,
then SD will increase.


If you add data that is closer to the mean,
then SD will decrease.
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by papgust » Mon Jun 14, 2010 6:38 am
If each term in a set is multiplied by a number greater than 1,
then SD will increase.


If each term in a set is multiplied by a number less than 1,
then SD will decrease.

----

If each term in a set is divided by a number greater than 1,
then SD will decrease.


If each term in a set is divided by a number that lies between 0 and 1,
then SD will increase.
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by papgust » Mon Jun 14, 2010 6:43 am
Does the change of signs in all terms of a set affects SD??

Answer is a simple NO. Change of signs has no bearing on the SD.
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by papgust » Mon Jun 14, 2010 6:47 pm
Calculating Average Speeds:

There are 2 ways to calculate average speeds,

1. Typical Distance-Time formula: (Traditional way - RECOMMENDED)

Assume S1 and S2 are the speeds of 2 trips. Distance d is the same for both the trips.
Assume T as the total time taken for both the trips.

Time taken = Distance / Speed.

For this scenario,

Total Time Taken = (Distance of Trip 1/Speed of Trip 1) + (Distance of Trip 2/Speed of Trip 2)

T = d/S1 + d/S2
T = (d*S1 + d*S2) / (S1*S2)
T = d*(S1+S2) / (S1*S2)

Now calculate Average speed using Total Distance and Total Speed,
Avg Speed = Total Distance / Total Time Taken

Avg Speed = 2d / T .......... [2d is the distance of Trip 1 and 2]

Sub. T = d*(S1+S2) / (S1*S2) in the equation,
Avg Speed = 2d*(S1*S2) / d*(S1+S2)
Avg Speed for the entire trip = 2*(S1*S2) / (S1+S2) .... [Cancelling out d]

NOTE: You don't need to solve this to get average speed. You can apply this formula straight away. Just wanted to show you how the formula is arrived.



2. A cool shortcut: (UNORTHODOX Approach)

Assuming Distance is the same for both the trips. S1 and S2 are the speeds of Trips 1 and 2.

Step i:
Form S1:S2 and reduce the ratio as much as possible to S3:S4.
Then, add the parts of ratio -- S3+S4

Step ii:
|S1-S2| / (S3+S4) = N

Step iii:
S1 + (S3*N) = Avg Speed for the entire trip.

Example:
Calculate Avg Speed of 20 mph and 200 mph

Step i:
20:200 = 1:10 = 1+10 = 11 parts.

Step ii:
|20-200| / 11 = 16.36

Step iii:
20 + (1*16.36) = 36.36 mph -- [Average Speed for the entire trip].
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by Testluv » Tue Jun 15, 2010 1:28 pm
Papgust: you are simply AWESOME!
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