CAT 2003 Slot 1 — QA Question 10
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 sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero?
Answer & solution
- A
1st
- B
9th
12th
- D
None of the above
Assume that the first term of the progression is a and the common difference is d.
âµ T3 + T15 = T6 + T11 + T13
∴ (a + 2d) + (a + 14d) = (a + 5d) + (a + 10d) + (a + 12d)
∴ a + 11d = 0
But, T12 = a + 11d
∴ The 12th term of an arithmetic progression is 0.
Hence, option (c).