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Explanation:

Let a be the number of projects in which only Gyani is involved, g be the number of projects in which only Buddhi is involved and c be the number of projects in which only Medha is involved.

From the data, d = 6

b + d = 14

∴ b = 8

Also, e = 3 and f = 2

It is given that

a + g = b + c + d + f

∴ a − c + g = 16                               … (i)

Number of projects involving more than 1 consultant = 6 + 8 + 2 + 3 = 19

∴ Total number of projects = 2 × 19 − 1 = 37

a + b + c + d + e + f + g = 2 × (b + d + e + f) − 1

∴ a + c + g = 19 − 1 = 18                … (ii)

Solving (i) and (ii), we get,

c = 1 and a + g = 17

∴ a cannot be determined uniquely.

Hence, option (d).

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