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Bunuel
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A computer software was tested 300 times before its release. 07 Dec 2021, 10:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

68% (02:18) correct 32% (02:58) wrong based on 212 sessions

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A computer software was tested 300 times before its release. The testing was performed in three stages of 100 tests each. The software failed 15 times in Stage I, 12 times in Stage II, 8 times in Stage III, 6 times in both Stage I and Stage II, 7 times in both Stage II and Stage III, 4 times in both Stage I and Stage III, and 4 times in all the three stages. How many times did the software fail in a single stage only?

(A) 9
(B) 10
(C) 13
(D) 15
(E) 17


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C
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A computer software was tested 300 times before its release. 07 Dec 2021, 12:20
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Attaching the solution done on notes


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ElninoEffect
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A computer software was tested 300 times before its release. 07 Dec 2021, 18:04
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Bunuel
A computer software was tested 300 times before its release. The testing was performed in three stages of 100 tests each. The software failed 15 times in Stage I, 12 times in Stage II, 8 times in Stage III, 6 times in both Stage I and Stage II, 7 times in both Stage II and Stage III, 4 times in both Stage I and Stage III, and 4 times in all the three stages. How many times did the software fail in a single stage only?

(A) 9

(B) 10

(C) 13

(D) 15

(E) 17


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Failed in Stage 1 = 15times |eq 1
Failed in Stage 2 = 12times |eq 2
Failed in Stage 3 = 08times |eq 3
Failed in S1 & S2 = 06times |eq 4
Failed in S2 & S3 = 07times |eq 5
Failed in S1 & S3 = 04times |eq 6
S1,S2 and S3 = 04times | eq 7

We need to find failure in single stages only.

Subtract eq 7 from eq 1 to eq 6
New values:
Failed in Stage 1 = 11times |eq 8
Failed in Stage 2 = 08times |eq 9
Failed in Stage 3 = 04times |eq 10
Failed in S1 & S2 = 02times |eq 11
Failed in S2 & S3 = 03times |eq 12
Failed in S1 & S3 = 00times |eq 13

Subtract eq 13 from 8 and 10
Subtract eq 12 from 9 and 10
Subtract eq 11 from 8 and 9

New values:
Failed in Stage 1 = 09times |eq 8
Failed in Stage 2 = 03times |eq 9
Failed in Stage 3 = 01times |eq 10

This gives us individual values
Adding them 9+3+1 =13 answer. C

Feel free to ask the justification of any step if required. :D
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A computer software was tested 300 times before its release. 04 Jan 2026, 09:47
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Bunuel
A computer software was tested 300 times before its release. The testing was performed in three stages of 100 tests each. The software failed 15 times in Stage I, 12 times in Stage II, 8 times in Stage III, 6 times in both Stage I and Stage II, 7 times in both Stage II and Stage III, 4 times in both Stage I and Stage III, and 4 times in all the three stages. How many times did the software fail in a single stage only?

(A) 9
(B) 10
(C) 13
(D) 15
(E) 17


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Deconstructing the Question
This is a 3-set Venn Diagram problem involving the number of software failures in three stages.

Given Data:
Total Failures in Stage I \((n(A)) = 15\)
Total Failures in Stage II \((n(B)) = 12\)
Total Failures in Stage III \((n(C)) = 8\)

Intersections:
Failures in both I and II \((n(A \cap B)) = 6\)
Failures in both II and III \((n(B \cap C)) = 7\)
Failures in both I and III \((n(A \cap C)) = 4\)
Failures in all three stages \((n(A \cap B \cap C)) = 4\)

Step 1: Calculate "Exactly Two Stages" Regions
We need to remove the triple intersection from the double intersections to find failures that happened in *exactly* two stages.
Exactly I and II only = \(6 - 4 = 2\)
Exactly II and III only = \(7 - 4 = 3\)
Exactly I and III only = \(4 - 4 = 0\)

Step 2: Calculate "Exactly One Stage" Regions
We subtract the shared regions (Exactly Two + Exactly Three) from the total of each stage.

Only Stage I:
\(15 - (\text{Only I &II}) - (\text{Only I &III}) - (\text{All 3})\)
\(15 - 2 - 0 - 4 = 9\)

Only Stage II:
\(12 - (\text{Only I &II}) - (\text{Only II &III}) - (\text{All 3})\)
\(12 - 2 - 3 - 4 = 3\)

Only Stage III:
\(8 - (\text{Only I &III}) - (\text{Only II &III}) - (\text{All 3})\)
\(8 - 0 - 3 - 4 = 1\)

Step 3: Sum the Single Stage Failures
Total single stage failures = \((\text{Only I}) + (\text{Only II}) + (\text{Only III})\)
Total = \(9 + 3 + 1 = 13\)

Answer: C
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