A battery manufacturer tested five prototype battery cells.

Question

https://gmatclub.com/forum/download/file.php?id=89766 A battery manufacturer tested five prototype battery cells. The cathode material in each prototype consisted entirely of recycled material and virgin material, in varying proportions. For each prototype, the horizontal axis shows the percentage of recycled material in the cathode (R), and the vertical axis shows the percentage of tested cells that met a performance standard after repeated charging cycles (P). The size of each bubble represents the prototype’s average energy capacity (E), with larger bubbles representing greater capacity. Select from each drop-down menu the option that completes the statement most accurately based on the information provided. If the graph were redrawn with the percentage of virgin material on the horizontal axis instead of the percentage of recycled material, GRAPH_1_PLACEHOLDER would remain unchanged. Let V equal the percentage of virgin material in each prototype. Since each cathode consists entirely of recycled and virgin material, R + V = 100. Based on the graph, there is GRAPH_2_PLACEHOLDER correlation between V and P. GMAT-Club-Forum-vkhtomsx.png

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=89766

A battery manufacturer tested five prototype battery cells. The cathode material in each prototype consisted entirely of recycled material and virgin material, in varying proportions.

For each prototype, the horizontal axis shows the percentage of recycled material in the cathode (R), and the vertical axis shows the percentage of tested cells that met a performance standard after repeated charging cycles (P). The size of each bubble represents the prototype’s average energy capacity (E), with larger bubbles representing greater capacity.

Select from each drop-down menu the option that completes the statement most accurately based on the information provided.

If the graph were redrawn with the percentage of virgin material on the horizontal axis instead of the percentage of recycled material,  GRAPH_1_PLACEHOLDER  would remain unchanged.

Let V equal the percentage of virgin material in each prototype. Since each cathode consists entirely of recycled and virgin material, R + V = 100. Based on the graph, there is  GRAPH_2_PLACEHOLDER  correlation between V and P.

Official Solution:

Drop-down 1:

Changing the horizontal axis from the percentage of recycled material to the percentage of virgin material would change the horizontal position of each bubble, since the percentage of virgin material is 100% minus the percentage of recycled material.

However, P is still the percentage of tested cells that met the performance standard, so the  vertical positions  of the bubbles would not change.

Similarly, E is still the average energy capacity, so the  sizes  of the bubbles would not change.

Therefore, the correct selection is  the vertical positions and sizes of the bubbles .

Drop-down 2:

From the graph, as R increases, P generally decreases. Thus, recycled material and performance have a negative correlation.

Since:

V = 100 - R

a prototype with a larger value of R has a smaller value of V. Therefore, when we replace R with V, the direction of the relationship reverses.

As V increases, P generally increases.

Therefore, there is  a positive  correlation between V and P.

Correct answer:

Drop-down 1: "the vertical positions and sizes of the bubbles"
Drop-down 2: "a positive"

officiisnobis · Answer

1. Vertical Position and sizes
2. A positive relationship

LongZero · Answer

could you explain why plz?
how is the correlation between two proportions positive, if V increases then P decreases? They cant both go the same way?

LogicDriven · Answer

Dropdown 1: only the vertical positions and sizes of the bubbles

Dropdown 2: a negative

shreyans0311 · Answer

Bunuel  for Drop down 1
why does horizontal positions of the bubble is wrong? Right now the graph shows bubbles at (100-virgin%). there would be no need to change the size of bubbles if we move them horizontally. Is this approach flawed?

zaturn · Answer

1. We know from the question that 'The cathode material....  consisted entirely of recycled material and virgin material '
so from 100% if recycle is 20% -> virgin is 80%, and vice versa.

Therefore, changing the horizontal axis from  R (recycle) -> V (virgin)  will make the bubbles reverse their orders without changing any other thing, including the performance standard (vertical axis) and avg. energy capacity (size)

Answer: vertical axis and size would remain unchanged

2. The question asks for the relationship between  V (virgin) and P (performance) .
We already know the relationship between R and V (R + V = 100%)
The graph shows that:
low R -> high P

This is equal to:
high V -> high P

Answer: positive relationship

egmat · Answer

Hi shreyans0311,

I see exactly where this is coming from. You're picturing each bubble as a fixed prototype, so it feels like the bubble should just "stay put" horizontally. But a bubble's  horizontal position is set by whatever value the x-axis is measuring , and that value changes when you switch the axis.

Right now the x-axis measures R.  Look at the leftmost bubble: it sits at  R = 15 , near the left edge. If you redraw the chart so the x-axis measures  V  instead, that same prototype's x-value becomes V = 100 - 15 = 85 - so the bubble jumps to the far  right  side of the chart. It's the same prototype, but its horizontal position has moved all the way across.

Run it across all five and you'll see them flip:

- R =  15  - V =  85 
- R =  30  - V =  70 
- R =  50  - V =  50  (the only one that stays put)
- R =  65  - V =  35 
- R =  85  - V =  15

So the horizontal positions  do  change ( four  of the  five  move). That's why "only the horizontal positions" and "horizontal and vertical positions" are both wrong.

What actually stays unchanged:

Vertical position (P):  how many cells met the standard doesn't depend on whether you  label  the composition as R or V. Same number, same height.

Bubble size (E):  average energy capacity is its own measurement - switching the x-axis label doesn't touch it.

You're right that there's no reason to resize the bubbles - and that instinct is correct! The size stays. The piece to fix is that  relabeling the x-axis from R to V forces each bubble to a new horizontal spot  (except the R =  50  one). That's why the answer is  the vertical positions and sizes  remain unchanged.

Answer: the vertical positions and sizes of the bubbles

egmat · Answer

Hi LongZero,

You're right to be careful here, and your instinct about the graph  is  correct: on the chart, as  R goes up, P goes down . The trap is that the question asks about  V , not R - and V moves in the  opposite  direction from R.

Where the reasoning slips

Your statement "if V increases then P decreases" is actually describing  R , not V. Remember  V = 100 - R , so V and R are mirror images: when one is high, the other is low.

Let me rewrite the five points using V. Reading off the bubbles (R, then P), and converting each with  V = 100 - R :

- R =  15 , P =  82  - V =  85 
- R =  30 , P =  70  - V =  70 
- R =  50 , P =  64  - V =  50 
- R =  65 , P =  46  - V =  35 
- R =  85 , P =  40  - V =  15

Now line them up from  low V to high V :

- V =  15  - P =  40 
- V =  35  - P =  46 
- V =  50  - P =  64 
- V =  70  - P =  70 
- V =  85  - P =  82

As V climbs, P climbs right along with it.  They do go the same way  - that's a  positive  correlation.

Why it flips

High V means low R. Low R is where P is highest (the top-left bubble). So more virgin material lines up with better performance. The negative trend you saw belongs to R and P; flipping to V flips the sign.

Quick rehearsal:  if A goes up while B goes down (negative), and  V = 100 - A , then C goes  up  when B goes up - so C and B are  positive . Swapping to the "complement" variable always flips the direction of the correlation.

Answer: the vertical positions and sizes of the bubbles

A battery manufacturer tested five prototype battery cells.

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