CAT 2003 Slot 1 — QA Question 5
Answer the following question based on the information given below.
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.
The number of non-negative real roots of 2x – x – 1 = 0 equals
Answer & solution
- A
0
- B
1
2
- D
3
2x − x − 1 = 0
∴ 2x = x + 1
This equation indicates the intersection of an exponential curve, lying in the I and II quadrants, and a straight line.
∴ It can have two intersection points at the most.
In this case, we can find two intersection points by trial and error as x = 0 and x = 1
∴ There cannot be any other point of intersection.
∴ The equation has 2 non-negative real roots.
Hence, option (c).