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Staphyk
In a particular GMAT test ,a candidate was required to pass all the four different sections: Quantitative reasoning ,verbal reasoning,Integrated reasoning,and Analytical writing Analysis. What number of ways can the candidate fail?

A. 16
B. 15
C. 14
D. 13
E. 12

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in each of the sections, the candidate will either pass or fail - hence, there are 2 possibilities related to every section.
    Thus total possible cases = 2 x 2 x 2 x 2 = 16

out of the 16 cases, in only 1 case the candidate will pass in all section, in every other case he will fail.

Hence, the number of ways in which he can fail = 16 - 1 =15 (option B)
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Deconstructing the Question
There are 4 sections.
Each section has 2 outcomes: pass or fail.
Total possible outcome combinations are \(2^4\).

We want the number of ways the candidate can fail (i.e., not pass all four).

Step-by-step
Total combinations:
\(2^4=16\)

Only 1 combination represents passing all four sections.

So number of ways to fail:
\(16-1=15\)

Answer: B
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