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Software Testing Stages Failures

XAT 2012 · Quantitative Ability & Data Interpretation · Medium · Set Theory

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A computer program was tested 300 times before its release. The testing was done 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 the software failed in a single stage only?

  1. A.

    10

  2. B.

    13

  3. C.

    15

  4. D.

    17

  5. E.

    35

Answer

B

Explanation

Let A,B,CA, B, C be failures in Stage I, II, III. Given:

  • n(A)=15,n(B)=12,n(C)=8n(A) = 15, n(B) = 12, n(C) = 8
  • n(A∩B)=6,n(B∩C)=7,n(A∩C)=4n(A \cap B) = 6, n(B \cap C) = 7, n(A \cap C) = 4
  • n(A∩B∩C)=4n(A \cap B \cap C) = 4 Only in Stage I = 15−(6+4−4)=915 - (6 + 4 - 4) = 9. Only in Stage II = 12−(6+7−4)=312 - (6 + 7 - 4) = 3. Only in Stage III = 8−(4+7−4)=18 - (4 + 7 - 4) = 1. Total in a single stage only = 9+3+1=139 + 3 + 1 = 13.

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