In the diagram, 14 nodes are represented by circles, and relationships

Question

https://gmatclub.com/forum/download/file.php?mode=view&id=51005 In the diagram, 14 nodes are represented by circles, and relationships among the nodes are indicated by arrows. Each arrow points from one node (the parent node ) to another node (the child node ). A positive numerical value is assigned to each node so that the value assigned to a parent node is exactly double the value assigned to its child node. The nodes labeled A through E are the principal nodes . Use the drop-down menus to create the most accurate statement based on the information provided. The value assigned to the principal node labeled GRAPH_1_PLACEHOLDER must be exactly double the value assigned to the principal node labeled GRAPH_2_PLACEHOLDER . ID: 100438 Fig.jpg

mevicks · Accepted Answer

Child Node (arrow head) = (1/2) of Parent node. 
Assign place values as under and solve.

The value assigned to the principal node labeled  D  must be exactly double the value assigned to the principal node labeled  A

ka47 · Answer

let the circle between B and C be X ,so C is 2X,as it is the parent circle of the first one ,then the circle down from C is 4X ,left from which is 8X ,the nD is 16X . On the other hand,B is 2X,left from B is 4X ,then A is 8X .
So D is double of A .

EMPOWERgmatRichC · Answer

Hi Rajibuddin,

This IR prompt is similar to a Quant PS Sequence question; you'll probably find it easiest to TEST VALUES to get to the correct answer.

Based on the description, we're told that when a node (a circle) has an arrow pointing to another node (another circle), there's a relationship between the two values. The first circle (the parent node) has a value that is DOUBLE that of the second circle (the child node; the one that is pointed TO).

As an example, look at the first 2 circles (the "A" and the one that "A" is pointing to). Those circles COULD have respective values of 2 and 1, 4 and 2, 6 and 3, 8 and 4, etc. To be fair, the prompt did NOT state that the values had to be integers, so we could have 3 and 1.5, 2.08 and 1.04, etc.

By extension, a longer "string" of nodes must also have values that DOUBLE from node to node. Notice the 3 circles (the "A", the "blank" and the "B"). Their respective values could be 4-2-1, 8-4-2, 12-6-3, 10-5-2.5, etc.

These examples are note-worthy in that they show how TESTing VALUES can help you to figure out the relationships of the various nodes. This question asks us to find 2 nodes - one that has DOUBLE the value of another.

Let's start with the 4th node (the one between the "B" and "C" nodes). Let's give THAT node a value of 1. DOUBLING each value as we go, we'd have....

1....2 (the "B" node)....4......8 (the "A" node)

Now, going in the other direction...
1....2 (the "C" node)....4....8.....16 (the "D" node)

From this, we can see that the "D" node is DOUBLE the "A" node.

Thus, the correct answer is  D and A .

GMAT assassins aren't born, they're made,
Rich

GMATCoachBen · Answer

Short video solution here (2:21):

https://www.youtube.com/watch?v=hqxsdlcojSA

mmdfl · Answer

gmatninja solved this one: https://youtu.be/tE0_JvDsRqc?list=PLiaK ... uFb&t=2293

Usernamevisible · Answer

Isn't this a question of luck, what if I start with a different node and keep on finding values.

how to tackle this, please help - how to know the right starting point

egmat · Answer

Hi Usernamevisible,

Good instinct to question this, but here's the reassuring part: it is not luck, and the starting node genuinely does not matter.

Notice what ka47 and EMPOWERgmatRichC did - they both picked the little circle between  B  and  C  and called it  1 . But they could have called  any  node  1  (or  x , or  100 ) and gotten the exact same final answer. Here's why.

Why the starting point is free

You are never assigning fixed numbers - you are assigning a  reference , and every other node is then  forced  relative to it by the doubling rule (parent =  2  x child). The diagram fixes all the  ratios  between nodes. Ratios don't care where you begin.

So whether you start at A, at D, or at some blank circle, the relationship  D = 2 x A  falls out every single time. The numbers scale up or down together; the  2 -to- 1  link between D and A stays locked.

Quick rehearsal to feel it

Take just the top-left chain: A - o - B, where each parent is double its child.

-  Start at B = 1:  the middle circle =  2 , so  A = 4 . Ratio A : B =  4 : 1 .
-  Start at A = 100:  middle =  50 , so  B = 25 . Ratio A : B =  4 : 1 .

Same ratio, totally different starting numbers. That's the whole idea.

How to pick a starting node in practice

Since any node works, just choose the one that makes the arithmetic cleanest - usually a node  many arrows can branch out from , so you multiply/divide by  2  in easy steps. Set it to  1 , walk the doubling rule outward to every principal node, then compare. You'll land on  D = 2A  no matter what.

Answer: Dropdown 1: D, Dropdown 2: A

In the diagram, 14 nodes are represented by circles, and relationships

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In the diagram, 14 nodes are represented by circles, and relationships

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