An author is writing a biography of a historical figure. As part of hi

Question

https://gmatclub.com/forum/download/file.php?id=82246 An author is writing a biography of a historical figure. As part of his research, the author tracked all descendants of the historical figure, displayed in the diagram. The regions in the ring bordering the innermost circle represent the historical figure's three children, all now deceased. Each region in the next innermost ring represents a child of the person represented by the adjacent region nearer the center of the diagram. These regions are marked alive if the corresponding person is now living, and are unmarked otherwise. Each region in the outermost ring lists the total number of living descendants of the person represented by the adjacent region nearer the center of the circle over the total number of descendants of that person. Select from each drop-down menu the option that creates the most accurate statement based on the information provided. Fifty percent of the living descendants of the historical figure are descendants of Child GRAPH_1_PLACEHOLDER and GRAPH_2_PLACEHOLDER % of that child's descendants are living. Official Mock 6 GMAT-Club-Forum-2kpmfzxw.png

HarshavardhanR · Accepted Answer

Hey adgarg , Sure. Happy to help! We are not actually dealing with fractions here per se. The fraction is merely how the data is presented to us (e.g. that outermost circle). What matters is what that data presented as a fraction represents. The same data can be presented without using fractions and we would arrive at the same answers. In other words, this is not a math problem where fractions need to be added (in which case one would look at lcm and making the denominator the same). This is a logic problem, where we use the data presented in fraction format to find what is asked. For instance, here is the same data, but I have avoided using fractions (to show that we are not dealing with fractions here!) https://gmatclub.com/forum/download/file.php?id=82342 To find what is asked, we first need to find (1) The number of living descendants of the historic figure, broken down to each child (1,2,3). (2) The total number of descendants of each child. This is not adding of fractions. This is manually counting living and total descendants from the data given (fraction/other formats!) Let me know if things are clear now! ___ Harsha GMAT-Club-Forum-6uqwez9s.png

theproductguy · Answer

Child 3 has 16 living descendants and 20 total. Which means the answer is 3 & 80%.

Posted from my mobile device

samarpan.g28 · Answer

The historical figure has a total of 46 descendants, out of which, child one has 9, child two has 7 and, child three has 16 living ones. The total living descendants are 9+7+16=32. Child three has 16 out of 32 living descendants so the first dropdown is 3. Total descendants of child three are 20 so 16/20 *100=80. This will be the answer in the second dropdown. GMAT-Club-Forum-k85vm1ko.png

adgarg · Answer

Can you please clarify how the the descendents are calculated from the outer circle? It is not very clear GMAT-Club-Forum-4a4xckfl.png

samarpan.g28 · Answer

Hi adgarg , if you need to find the immediate descendants i.e. in second circle, you just have to count the parts that match the same colour as first circle. So for child 1 it is 3. For the third circle, just count the numbers in denominator under same colour group. Make sure that the numerator is descendants who are alive. Please let me know if this is understandable. Posted from my mobile device GMAT-Club-Forum-tvy7jv5v.png

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=82339 ___ Harsha GMAT-Club-Forum-1nwkhmbf.png

adgarg · Answer

Can you clarify why are we adding fractions directly without taking LCM first and making the denomitor the same? GMAT-Club-Forum-0gy846o9.png

RahulRajBasnet · Answer

living descendants of Child 3 is 13 , out of 16 total descendants, similarly Child 1 and 2 has 7 and 6 respectively, thus total living is equal to 13+7+6=26, and child 3 has 13 out of 26 living descendants, thus 50% of the historical figure living descendants are from Child 3, And 13 out of 16 descendants of Child 3 are living, thus approx. 80% percent.

elele · Answer

Does anyone have any advice on how to quickly understand and interpret a graphic like this? This is the first time I've seen this kind.

aakarsh1001 · Answer

RahulRajBasnet  Hey, for the second part, wouldn't it be 16/20 i.e 80%? 13 (from 3rd rind)+3 (from middle ring)/16+4?

cheshire · Answer

yeah i agree, it should be 16/20

Tucky · Answer

Hey  HarshavardhanR 
I am having lil problem with this Ques because of the so many convoluted rings. Haha

Each region in the outermost ring lists the total number of living descendants of the person represented by the adjacent region nearer the center of the circle over the total number of descendants of that person."

My understanding is: for Child 1, 1/2 represents:   number of living descendants of C/ total number of descendants of that person.

I don't understand then 1/2 and 6/7 doing in CHILD1. I am sure, my understanding is incorrect. Please help.

HarshavardhanR · Answer

Sure! Happy to try and help.

Short Answer:  Yup, I think you have misinterpreted this!

Specifically  ->

The outermost ring gives details of the descendants of the person(s) in the middle ring specifically, not directly Child 1 (or 2 or 3).

Long Answer:  Keep the diagram close. Observe the points below against the diagram. We will take the example of  Child 1  to understand the data.

- Innermost circle: The historical figure. Dead.
- Innermost ring: The three children of the historical figure. All 3 dead. 
- Now - focus on  Child 1  (Red).
- Middle ring: 3 regions in total, 2 have "alive" and 1 is blank. 
- This means that  Child 1  had 3 kids - 2 of them are still alive. One is dead. Let's call them  Alive 1 ,  Alive 2 , and  Dead Guy .
- Now, let's focus on the outermost ring.
- 0/0 --- means that  Alive 1  had no children at all. 
- 1/2 --- means that  Alive 2  had 2 children. 1 of them is alive, the other is dead.
- 6/7 --- means that  Dead Guy  had 7 children (conceived when the Dead Guy was still alive, obviously!). 6 of them are still alive, 1 is dead.

Hope this helps!
Harsha

AnushkaKala · Answer

hey! thank you for explaining here, this was quite helpful. i didnt understand how child 3's further generation's live count is 13 and not 9+3 aka 12? (9 from outermost ring & 3 from the one inside it? 
also, how is 4/4 counted? 4 kids, all died?

HarshavardhanR · Answer

Hey,

Sure. Let me explain!

Let's focus on Child 3.

- Innermost circle --- Child 3: Dead 
- Middle Ring --- Child 3 has 4 children: 3 alive, 1 dead.  Live Count so far : 3

This sentence is important ---  " Each region in the outermost ring lists the total number of  living descendants  of the person represented by the adjacent region nearer the center of the circle  over  the  total number of descendants  of that person."
  
i.e., 4/4 means that --- that one descendant of Child 3 who is now dead had 4 children - all 4 of them are still alive.

-  Outermost ring  --- (2/2, 4/4, 5/7, and 2/3) --- means (2+4+5+2 = 13 alive) out of (2+4+7+3 = 16 total).

So, Number of living descendants from Child 3 = 3 + 13+16.

Hope this helps!

eaat · Answer

HarshavardhanR  Why do we count only the dropdown 1 or part 1, and the outer 2 rings for dropdown 2?

Adit_ · Answer

I can maybe try to help the gist of what is happening,
So basically the outer most ring is No.of living/Total people that a person gave birth to just inner to the outer most ring.

Child 3 is having 3 "alive" inner rings if you notice. Each of these 3 consider them as 1 person each, and each has given birth to "x" number of people out of which "y" number of people are still living.
Which mean y/x is the ratio of Alive/Total given birth by each of the inner rings.

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