Logical Reasoning Discussion

**Common Information**

New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha is involved.

All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani and 3 projects with Gyani but without Medha.

The total number of projects for New Age Consultants is one less than twice the number of projects in which more than one consultant is involved.

Q. |
What is the number of projects in which Medha alone is involved? |

✖ A. |
Uniquely equal to zero |

✔ B. |
Uniquely equal to 1 |

✖ C. |
Uniquely equal to 4 |

✖ D. |
Cannot be determined uniquely |

**Solution:**

Option(**B**) is correct

Consider the Venn diagram shown below.

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

As *c* = 1

∴ Number of projects in which Medha alone is involved = 1

Hence, **option B** is the correct choice.