A conservation lab processes archival photographs through the stages

Question

https://gmatclub.com/forum/download/file.php?id=89876 A conservation lab processes archival photographs through the stages shown in the flowchart. Each rectangular box represents a distinct processing stage, while each diamond represents a decision point and is not counted as a stage. The time required for each stage is shown in minutes, and there is no waiting time between stages. The conditional stages are additional cleaning and a second color scan, each of which is performed only when required. One-half of all photographs are sufficiently clean after the initial cleaning and do not require additional cleaning. Of all photographs, 40% require a second color scan. From each drop-down menu, select the option that creates the most accurate statement based on the information provided. The average amount of time spent in conditional stages per photograph is GRAPH_1_PLACEHOLDER minutes. The average number of conditional stages undergone per photograph is GRAPH_2_PLACEHOLDER . GMAT-Club-Forum-qmwgcs7k.png

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=89876

A conservation lab processes archival photographs through the stages shown in the flowchart. Each rectangular box represents a distinct processing stage, while each diamond represents a decision point and is not counted as a stage. The time required for each stage is shown in minutes, and there is no waiting time between stages. The conditional stages are additional cleaning and a second color scan, each of which is performed only when required.

One-half of all photographs are sufficiently clean after the initial cleaning and do not require additional cleaning. Of all photographs, 40% require a second color scan.

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

The average amount of time spent in conditional stages per photograph is  GRAPH_1_PLACEHOLDER  minutes.

The average number of conditional stages undergone per photograph is  GRAPH_2_PLACEHOLDER .

Official Solution:

Drop-down 1:

There are two conditional stages: additional cleaning and a second color scan.

One-half of all photographs do not require additional cleaning, so the other half do require it. Additional cleaning takes 16 minutes. Thus, its average contribution to the time spent in conditional stages per photograph is:

1/2 * 16 = 8 minutes

Also, 40% of all photographs require a second color scan, which takes 20 minutes. Thus, its average contribution is:

0.40 * 20 = 8 minutes

Therefore, the average amount of time spent in conditional stages per photograph is:

8 + 8 = 16 minutes

Therefore, the correct selection is 16.

Drop-down 2:

A photograph can undergo zero, one, or two conditional stages. However, these possibilities do not occur with equal frequency, so simply averaging zero, one, and two would not give the required average.

One-half of all photographs undergo additional cleaning. Therefore, this stage contributes an average of:

1/2 = 0.50 stage per photograph

Also, 40% of all photographs undergo a second color scan. Therefore, this stage contributes an average of:

0.40 stage per photograph

Thus, the average number of conditional stages undergone per photograph is:

0.50 + 0.40 = 0.90

For example, among 100 photographs, 50 would undergo additional cleaning and 40 would undergo a second color scan. This gives 90 conditional-stage occurrences across 100 photographs, for an average of:

90/100 = 0.90

It does not matter whether some photographs undergo both conditional stages. A photograph that undergoes both contributes two conditional-stage occurrences, so the total number of occurrences remains 50 + 40 = 90.

Therefore, the correct selection is 0.90.

Correct answer:

Drop-down 1: "16"
Drop-down 2: "0.90"

hd29 · Answer

The average amount of time spent in conditional stages per photograph is (16x0.5 + 20x0.4) = 16 minutes.

The average number of conditional stages undergone per photograph is (0.5+0.4)/1 = 0.9

A conservation lab processes archival photographs through the stages

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Graphs and Tables (G&T) Questions

A conservation lab processes archival photographs through the stages

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards