IR Graph Question Bank #1

[sophia.lin12345]

http://www.manhattangmat.com/images/CAT/IR/Chemical-Flow.png

In the flowchart, each rectangular box represents a distinct stage in the production of a 50-kilogram batch of a specialty chemical. Decision points, which are not distinct stages, are represented by diamond shapes. The time required for each stage is indicated in minutes (min). There is no waiting time between stages. Three quarters of all batches do not require additional heating, while half of all batches require a second mixing with hydrochloric acid (HCL); none require a third.

From each drop-down menu, select the option that creates the most accurate statement based on the information provided.

The average time for a batch of ingredients to make it all the way through the process shown is ? minutes.

The average number of stages that a batch undergoes is ?

SOLUTION:

Statement 1: 140 minutes. The easiest way to find the average time is to "weight" every stage’s time by the percent of batches that undergo that stage, then add up all those weighted times.
1) Heating at 200K: all batches go through this stage, so the 30 minutes remains the same (100% of 30 = 30).
2) Additional heating: only one quarter (1/4) of batches go through this stage, since three quarters (3/4) do not require additional heating. (Be careful not to misread this! You might miss the "not.")
One quarter is 25%; 25% of 20 minutes = 5 minutes.
3) Sifting: all batches go through. Keep the full 5 minutes.
4) First HCL mixing: all batches go through the first time. Keep the full 20 minutes.
5) Second HCL mixing: only half (50%) of batches require this repetition, so 50% of 20 minutes = 10 minutes. No batches require any more HCL mixing, so you can move on.
6) Filtration: Full 10 minutes.
7) Drying: Full 60 minutes.

Sum all the weighted times: 30 + 5 + 5 + 20 + 10 + 10 + 60 = 140 minutes.

Statement 2: 5.75 stages. You can do the same thing with the number of stages"”just count each stage a full "one time" if 100% of batches go through it, and as a fractional or decimal stage if less than 100% of batches go through.
1) Heating: 1 stage
2) Additional heating: 0.25 stages(again, be careful not to misread as 0.75 stages)
3) Sifting: 1 stage
4) First HCL mixing: 1 stage
5) Second HCL mixing: 0.5 stages
6) Filtration: 1 stage
7) Drying: 1 stage

Sum all the weighted stages: 1 + 0.25 + 1 + 1 + 0.5 + 1 + 1 = 5.75 stages.

[sophia.lin12345]

Just to make sure I'm interpreting this correctly, when we find the average number of stages, the additional heating counts as 0.25 because only one quarter of all batches actually require additional heating. Technically, since the rest of the batches don't actually need additional heating, that is actually counted as 3/4*0=0, so that's why the solution doesn't include that. Is this right?

Finally-which questions in the OG, online question bank, or practice CAT could I also refer to that would use the method that the solution uses to find the average?

[tim]

You are correct in your reasoning. I didn't see a question in your first post, but if there is one please repeat it so we can help you with it. This type of question would typically be categorized as a weighted average in the GMAT literature, but it is more commonly referred to as expected value in real life. A search for either of those terms should help you find more problems of this type.