GMAT Math

Another point to remember:

Example:

-1/10 < n < 1/10

After taking reciprocal of n, FLIP SIGNS!

-10 > n > 10

Hi Papgust,

Wonderful tips!! Please keep posting.

Regards,
Viju

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.

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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.

I really appreciate your effort..Thanks a lot !!
I am following it everyday..

sumanr84 wrote:I really appreciate your effort..Thanks a lot !!
I am following it everyday..

I'm flattered..! Thank you

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.

--[ 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.

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.

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].

Papgust: you are simply AWESOME!