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 involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with 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.
What is the number of projects in which Medha alone is involved?	Answers
A) Uniquely equal to zero B) Uniquely equal to 1 C) Uniquely equal to 4 D) Cannot be determined uniquely E) None of these
Explanation :   It is given that all the three consultants are involved in 6 projects together. So put 6 where all the three circles intersect.   Buddhi has 2 projects with Medha but without Gyani. i.e., Medha and Buddhi alone worked in 2 projects.   Also given, Buddi worked on 3 projects with Gyani but without Medha. i.e., Buddi and Gyani alone worked on 3 projects.   Gyani worked with Medha in 14 projects. These two worked together along with Buddhi in 6 projects. So Gyani and Medha alone worked on 14 - 6= 
<gadget id="calculator">14 - 6</gadget>
<output>8</output>
8 Projects.   Lets us assume, Gyani, Buddhi and Medha alone worked on a, b, c projects.   It was given that The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of projects in which Medha involved.=&gt; a + b = 8 + 6 + 2 + c   =&gt; a + b = 16 + c ------------------ (1)   Also given 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.   The projects in which more than 1 consultant involved = 6 + 3 + 2 + 8= 
<gadget id="calculator">6 + 3 + 2 + 8</gadget>
<output>19</output>
19.   Total projects= a + b + c + 8 + 3 + 2 + 6 = a + b + c + 19   =&gt; 2 × 19 - 1 = a + b + c + 19.   =&gt; a + b + c = 18.   =&gt; a + b = 18 - c.   Substituting this value in equation (1) we get,   =&gt; 18 - c = 16 + c.   =&gt; c = 1.   Answer : Uniquely equal to 1
<result>B</result>
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 involved. All three consultants are involved together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with 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.
What is the number of projects in which Medha alone is involved?