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What you choose is what you weigh- An e-GMAT Article

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What you choose is what you weigh- An e-GMAT Article [#permalink] New post 10 Dec 2012, 07:22
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Hi folks,

As we experience, life is all about laying priorities & importance to the things that affect our life. ‘Importance’ in mathematical parlance is referred to as‘Weight’.

It depends on an individual ‘how much weight one places on making a choice?’

Be it choosing a car or a would-be-spouse, we assign different weights to different attributes. Hope you guys don’t mind if I discuss this aspect using an example of buying a car instead of selecting a would-be-spouse.



Say John wishes to buy a car. He lays importance to 2 attributes—Mileage & Power. He narrows down his choice to two brands of car.
Assume on a score of 10, Brand A scores 8 on mileage & brand B scores 6. While on a similar scale; Brand A scores 6 on Power & brand B scores 8.

It is obvious that if John weighs Mileage & Power equally, then it is difficult for him to choose one brand of car over the other. While Brand B scores better in case of Power, Brand A excels in terms of mileage.
Practically speaking, we seldom lay equal importance to all attributes. For people who really care for the weight of their pocket, mileage will be more important than power, while for adventure loving people, it will just be the reverse.

Our friend John is an adventure loving guy, who reckons Power to be relatively more important than Mileage. He lays 60% weight to Power and 40% to Mileage. So here, the scenario will look like this.
Image

Now, in this case, John will clearly prefer Brand B over Brand A since Brand B scores more in terms of Power, which is a more important attribute for him.

But David, another friend of ours, shares a different opinion than John’s. Because he drives a lot on a daily basis, he sets his priority to the brand that gives him value-for-money.
He lays 40% weight to Power, & 60% to Mileage. So for him, the scenario will look like this.

Image

It is quite obvious that David will buy brand A rather than brand B.

In this world, there are varied needs of individuals, hence there are multiple brands that co-exist due to different weights assigned by each individual to different needs.

So let’s see how John rates the two brands for cars mathematically. For brand A, contribution of mileage is 40% of 8, equaling to 3.2. Similarly, contribution of power is 60% of 6, equaling to 3.6. So John rates Brand A at 3.2 + 3.6 = 6.8.
For Brand B, contribution of mileage is 60% of 8, equaling to 4.8 and of power is 40% of 6, equaling to 2.4. So John rates brand B as 4.8 + 2.4 = 7.2.

Now, these final rates of both brands of cars are in fact called ‘Weighted Average’.

Well friends, life is not that easy. We frequently come across situations, where a choice may involve multiple attributes with varied importance.But the good news is that even with such plethora of choices, we can easily derive “Weighted Average” with the help of this formula.

Consider a dataset with n attributes with their values:

The weighted average would be calculated as follows.

Image

Now let’s consider an example with more than 2 attributes. Say another person, Joe, considers 5 attributes to buy a car; Mileage, Power, Cost, Service, & Safety.
He assigns relative weights to each attribute as given in the table below (The table also mentions the ratings of 3 brands based on these attributes).

Image


Image

For Joe, the final rating for Brand A would be = (8 *20 + 6 *20+8 *15 + 5 *15+6*30 )/100= 6.55
Similarly, brand B rates 6.7 and brand C rates 6.1.

Let’s orient our thinking as to how GMAT tests this concept. Let’s discuss one dataset which uses Weighted Average concept in a slightly different way.

‘For its 4-year Bachelor of Engineering (BE) program, the college proposes to the Student Union two-options to determine final score. In these two approaches, the college wishes to weigh each year marks differently.
Given below are the two suggested options along with sample percentage marks of a student for each year.’

Image

For each of the following statements, select ‘Yes’ if statement is true based solely on the information provided in the table; otherwise select ‘No’.

1. If sample marks are taken into account, then Option 1 is more favorable to the Student Union.
2. If sample marks are taken into account, then calculating the final score as the median of marks is more favorable to the Student Union than opting for Option 1.
3. Students who expect to score higher marks in their 4th Year as compared to other 3 years should prefer Option 1 over Option 2.


Understand the dataset

Let’s first understand the data set. When we look at the dataset, we should register following aspects in our mind.
The data set is about a 4-year college program. As the table shows, marks are allocated each year. The college has suggested two approaches to determine the final score of students. The options vary in terms of the weightage assigned to marks each year to calculate the final marks of each student. We have also been provided with 1 set of marks for a student.

Let’s just view a few data points. Weight-age means importance given to a certain value. In the present example, we can infer that 1st year sample marks carries an importance of 10% only compared to 50% for 4th year marks as per option ‘1’. Note, both columns 3 and 4 individually add up to 100%. This means that for computation of final marks, first year contribution is 7.5(10% of 75), whereas 4th year contribution is 41(50% of 82).

Another interesting aspect is that we can expect students who score less in final year to prefer option 2 over option 1. It is because option 2 lays 10 percentage points more weightage than option 1 for the marks earned in the 4th year.

Question 1 Statement

If sample marks are taken into account, then Option 1 is more favorable to the Student Union.

Understand the Question

Let's understand the first question statement. We have to find whether this statement is true or false per the information in the dataset. Now this question statement does not directly provide us with the mathematical relationship. We need to contextualize this statement.

What will the Student Union or students favor more? It will be the option that helps them score higher final marks given their scores in each of the 4 years. So clearly, the answer to this question statement is YES if the final score per option 1 is greater than the final score per option 2. The mathematical equation is presented below.

Is Final Score|Option 1 > Final Score|Option 2 ?

And we need to calculate this final score using the sample % marks that we have been provided in the table.

Image


Approach

1. Calculate relative weightage percentage points for option 1 over option 2
a. Column 5 =Column 3 - column 4
2. Calculate relative more/less Final Score of option 1 over option 2
a. Column 2 & 5, & Apply
Image
3. If calculated value in step 2.a is more than 0, answer is YES, else NO.

Solve-Apply Approach

So now let’s come up with the approach to solve this question.

Let’s understand the question again; we need not calculate the final scores via option 1 & 2.

The question asks us ‘Is option 1 final score relatively more than final score via option 2?’

So we simply calculate how much option 1 weight-age is more or less than option 2 relatively. This will save our precious time of calculating final scores twice i.e. final score for both the options, & then compare their scores.
Let’s put our findings in column 5.

Image

Relative more or less Final year score =

Image

We could have excluded year 1 calculation, as the relative weight-age of option 1 over option 2 is 0. It will not have any impact on final score calculation.
0% means that while calculating final year marks, option 1 does not weigh more or less compared to option 2. Final scores via both the options are equal. Hence the answer to this question statement is NO.

Should you wish to look at an interactive audio visual solution of this question, & the subsequent 2 more questions, you may click at ‘START FREE TRIAL’.

We realize that it is the time to address the need of the test takers to attempt variety of IR questions that are true reflection of Official Guide questions.
e-GMAT has launched 15+ hours of interactive audio visual content on IR. It encompasses 35 concepts, 120+ original questions, and 2 full length Mock Tests.

We appreciate if you attempt the question, & provide us feedback. We at e-GMAT constantly strive for excellence in learning pedagogy.

Here we sign off with 2 questions for you to attempt ( Given in dataset).

Happy Reasoning!

-Shalabh Jain
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Last edited by egmat on 31 Jul 2013, 13:13, edited 2 times in total.
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 13 Dec 2012, 20:27
hey

2) Median for this data set = 82

Whereas using option 1 the value comes out to be 81.5

Since 82>81.5

So, answer for question 2 is YES.

3) A clear YES, without any calculations. The higher the weightage for fourth year, more favorable it is for the student with more marks in that year.
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 13 Dec 2012, 22:25
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pashraddha wrote:
hey

2) Median for this data set = 82

Whereas using option 1 the value comes out to be 81.5

Since 82>81.5

So, answer for question 2 is YES.

3) A clear YES, without any calculations. The higher the weightage for fourth year, more favorable it is for the student with more marks in that year.


Hi Prashraddha,

Q1. Median for this data set would be 81 [(80+82)/2];

Now, Median (81) < Final score, as per option 1(81.5), hence answer is NO.


Q2. Well this question certainly demands more analysis. We cannot mere consider the weight-age of option 1 & option 2 for 4th year, & jump to the conclusion.

Though weight-age of option 1 (50%) > Weight-age of option 2 (40%) for 4th year, the weight-age of option 1 (15%) < Weight-age of option 2 (20%) for 2nd year, & the weight-age of option 1 (25%) < Weight-age of option 2 (30%) for 3rd year.

For 4th year, option 1 is favorable, but for 2nd, & 3rd year, option 2 is favorable. We should also consider this aspect too.

Now, can you come up with an answer?

-Shalabh :)
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 13 Dec 2012, 22:57
Oops I don't know how I got median wrong :oops:

Still the answer for third question should be a YES. A student with comparatively less % in other 3 years and higher % in 4th will find Option 1 favorable.
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 14 Dec 2012, 22:27
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pashraddha wrote:
Oops I don't know how I got median wrong :oops:

Still the answer for third question should be a YES. A student with comparatively less % in other 3 years and higher % in 4th will find Option 1 favorable.


Hi,

Its correct, the answer to question 3 is YES only.

Just look at the analysis for more clarity.

First year score does not carry any significance, as the weight-ages for option 1 & 2 are 10% each. So no option will have an edge over the other.

Now, say the scores in II, III, & IV years are x, y, & z respectively.

Since weigh-ages for II, III year are more for option 2 over option 1, hence the 'Total gain for option 2 over option 1 for II & III' = (20-15)% of X + (30-25)% of Y = 5% of (X+Y)

Conversely, since weigh-ages for IV year is more for option 1 over option 2, hence the 'Total gain for option 1 over option 2 for IV' = (50-40)% of Z = 10% of Z

Now, we have compare 5% of (X+Y) against 10% of Z.

If 5% of (X+Y) [b]< 10% of Z[/b], then the answer is YES, else No.

So the inequality/equality is 5% of (X+Y) < = > 10% of Z ? This can be reduced to X+Y < = > 2 Z ?

Now, we know that as per the question, the student scores more marks compared to other year marks, it means Z > X, & Z > Y as well.

So it is obvious that X+Y < 2 Z. So the answer is YES.

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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 17 Dec 2012, 18:08
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Hi Shalabh,
Nice question it was..Please come up with some more of these.

Ans : 1-N ,2-N, 3-Y

However, for Qs.2, can you please let me know that how the median is getting calculated as I'm not getting it as 81 but as 80.25.
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 18 Dec 2012, 06:01
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debayan222 wrote:
Hi Shalabh,
Nice question it was..Please come up with some more of these.

Ans : 1-N ,2-N, 3-Y

However, for Qs.2, can you please let me know that how the median is getting calculated as I'm not getting it as 81 but as 80.25.


Hi Debayan,

The median for individual numbers are calculated as the middle-most value of datatset, provided dataset is arranged in ascending order.

In Q 2, the 4 sample marks, when arranged in ascending order will look like 75, 80, 82, & 84. Here, we find that there is no middle-most term. So we take average of 2 middle-most terms i.e. 80 & 82. So the Median is (80+82)/ 2 = 81.

Median Calculation:--

Say the dataset includes 'n' values.

If n is odd, then the median of this dataset will be the value at (n + 1)/2 location when the data is arranged in ascending order.

If n is even, then the median of this dataset will be the average of two values. Value 1 at n/2 location and value 2 at n/2+1 location, when the data is arranged in ascending order.


Hope this is clear to you. :)

-Shalabh
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 18 Dec 2012, 20:58
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Hello friends,

What could be the answer to question 3- Students who expect to score higher marks in their 4th Year as compared to other 3 years should prefer Option 1 over Option 2? if following changes were made.

Image

-Shalabh
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 18 Dec 2012, 21:56
My quick guess will be that it has no effect. The reason is as follows:

The 2Z <=> X + Y inequality/equality that you previously generated will convert into Z <=> 0.4X + 0.6Y

Now if Z > X and Z > Y,
=> 0.4Z > 0.4X and 0.6Z > 0.6Y
=> Adding them up => Z > 0.4X + 0.6Y

So in every possible scenario, Z is always greater than 0.4X+0.6Y. (Z == 0.4X+0.6Y only when X = Y = Z)

Please let me know if am missing anything.
Thanks.
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 19 Dec 2012, 20:55
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abikumar wrote:
My quick guess will be that it has no effect. The reason is as follows:

The 2Z <=> X + Y inequality/equality that you previously generated will convert into Z <=> 0.4X + 0.6Y

Now if Z > X and Z > Y,
=> 0.4Z > 0.4X and 0.6Z > 0.6Y
=> Adding them up => Z > 0.4X + 0.6Y

So in every possible scenario, Z is always greater than 0.4X+0.6Y. (Z == 0.4X+0.6Y only when X = Y = Z)

Please let me know if am missing anything.
Thanks.



That's correct Abhi. You hit it right.Your concepts are clear. Did you try this one? a-question-on-multiple-graph-charts-with-varied-weights-143337.html

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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 19 Dec 2012, 21:19
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egmat wrote:
debayan222 wrote:
Hi Shalabh,
Nice question it was..Please come up with some more of these.

Ans : 1-N ,2-N, 3-Y

However, for Qs.2, can you please let me know that how the median is getting calculated as I'm not getting it as 81 but as 80.25.


Hi Debayan,

The median for individual numbers are calculated as the middle-most value of datatset, provided dataset is arranged in ascending order.

In Q 2, the 4 sample marks, when arranged in ascending order will look like 75, 80, 82, & 84. Here, we find that there is no middle-most term. So we take average of 2 middle-most terms i.e. 80 & 82. So the Median is (80+82)/ 2 = 81.

Median Calculation:--

Say the dataset includes 'n' values.

If n is odd, then the median of this dataset will be the value at (n + 1)/2 location when the data is arranged in ascending order.

If n is even, then the median of this dataset will be the average of two values. Value 1 at n/2 location and value 2 at n/2+1 location, when the data is arranged in ascending order.


Hope this is clear to you. :)

-Shalabh


Hi Shalabh,
Thanks for the clarification and reminding me how to calculate median.. :) Actually I got confused with 'mean/average' and 'median' calculations.

However,a quick qs. on your explanation above :
1. You've mentioned "...when the data is arranged in ascending order."; I think order can be anything, I mean either ascending or descending. Your thoughts..?

BTW,answers will be same as mentioned above in my last post.Please confirm.
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 19 Dec 2012, 22:19
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egmat wrote:
Hello friends,

What could be the answer to question 3- Students who expect to score higher marks in their 4th Year as compared to other 3 years should prefer Option 1 over Option 2? if following changes were made.

Image

-Shalabh


The marginal weight-age increase in 3rd year and marginal decrease in 2nd year for option 2,don't change the fact that in Option 2, students in 4th year are still getting less marks as compared to other 3 years,whereas in option 1 it remains the same(i.e 4th year weight-age marks >3 years weight-age marks) so option 1 is still preferable for them.

Hope this makes sense.. :)
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 08 Jan 2013, 22:29
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The marginal weight-age increase in 3rd year and marginal decrease in 2nd year for option 2,don't change the fact that in Option 2, students in 4th year are still getting less marks as compared to other 3 years,whereas in option 1 it remains the same(i.e 4th year weight-age marks >3 years weight-age marks) so option 1 is still preferable for them.

Hope this makes sense.. :)[/quote]

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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 08 Jan 2013, 22:33
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debayan222 wrote:
egmat wrote:
debayan222 wrote:
Hi Shalabh,
Nice question it was..Please come up with some more of these.

Ans : 1-N ,2-N, 3-Y

However, for Qs.2, can you please let me know that how the median is getting calculated as I'm not getting it as 81 but as 80.25.


Hi Debayan,

The median for individual numbers are calculated as the middle-most value of datatset, provided dataset is arranged in ascending order.

In Q 2, the 4 sample marks, when arranged in ascending order will look like 75, 80, 82, & 84. Here, we find that there is no middle-most term. So we take average of 2 middle-most terms i.e. 80 & 82. So the Median is (80+82)/ 2 = 81.

Median Calculation:--

Say the dataset includes 'n' values.

If n is odd, then the median of this dataset will be the value at (n + 1)/2 location when the data is arranged in ascending order.

If n is even, then the median of this dataset will be the average of two values. Value 1 at n/2 location and value 2 at n/2+1 location, when the data is arranged in ascending order.


Hope this is clear to you. :)

-Shalabh


Hi Shalabh,
Thanks for the clarification and reminding me how to calculate median.. :) Actually I got confused with 'mean/average' and 'median' calculations.

However,a quick qs. on your explanation above :
1. You've mentioned "...when the data is arranged in ascending order."; I think order can be anything, I mean either ascending or descending. Your thoughts..?

BTW,answers will be same as mentioned above in my last post.Please confirm.


Hi Debayan,

Yes, you are right. Data can be arranged in ascending or descending order. However in GMAT exam, you will be able to sort in ascending order only. :)

-Shalabh Jain
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 20 Jan 2013, 22:19
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Hello all,

Pl. try these 3 tricky questions on weighted average- Fresh from e-GMAT bakery.
a-fresh-tricky-ta-dataset-on-weighted-average-146116.html

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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 28 Jan 2013, 23:31
thank you e gmat expert.
I already understand weighed average.

but dose this concept is tested on IR section ?

I do not see this concept is tested on gmatprep. is my thinking correct?
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 29 Jan 2013, 02:07
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thangvietnam wrote:
thank you e gmat expert.
I already understand weighed average.

but dose this concept is tested on IR section ?

I do not see this concept is tested on gmatprep. is my thinking correct?

Hi,

Please refer to question #20A of OG13. It tests weighted average concept. Pl. attempt the question of better understanding.

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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 29 Jan 2013, 02:16
I have pdf version of og 13 but do not see the question you mention.

at what page dose that question is? pls help

pls help, dose this pdf version is not good?
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Re: What you choose is what you weigh- An e-GMAT Article [#permalink] New post 29 Jan 2013, 03:11
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thangvietnam wrote:
I have pdf version of og 13 but do not see the question you mention.

at what page dose that question is? pls help

pls help, dose this pdf version is not good?

Hi,

This is not given in pdf version. I have attached the question for your ready reference.

-Shalabh
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Re: What you choose is what you weigh- An e-GMAT Article   [#permalink] 29 Jan 2013, 03:11
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What you choose is what you weigh- An e-GMAT Article

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