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CAT 1996 — QA Question 32

Arithmetic ProgressionEasy
Passage / Data

Answer the questions based on the following information.

A series S1 of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series S2, the nth term defined as the difference between the (n + 1)th term and the nth term of series S1, is an arithmetic progression with a common difference of 30.

First term of S1 is

Answer & solution

  • A

    80

  • B

    90

  • 100

  • D

    120

Solution

First series: (S1) = x, y, x2, z, x + 20

Second series: (S2) = a1, a2, a3, a4

Now a1 = y – x, a2 = x2 - y, a3 = z - x2 and a4 = x + 20 – z

a2 – a1 = 30 gives 3x – 4y = 60 ... (1)

a4 – a3 = 30 gives 3x – 4z = 20 ... (2)

and a4 – a2 = 60 gives x – 2z + 2y = 80 ... (3)

Solving these equations we get the values of x = 100, y = 60, z = 70

∴ S1 is 100, 60, 50, 70, 120

S2 is –40, –10, 20, 50.

Hence, option (c).

CAT 1996 QA Q32: First term of S 1 is — Solution | TheCATExam