CAT 1996 — QA Question 48
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.
Which of the following values of x do not satisfy the inequality (x2 – 3x + 2 > 0) at all?
Answer & solution
1 ≤ x ≤ 2
- B
–1 ≥ x ≥ –2
- C
0 ≤ x ≤ 2
- D
0 ≥ x ≥ –2
If we simplify the expression x2 – 3x + 2 > 0, we get (x – 1)(x – 2) > 0. For this product to be greater than zero, either both the factors should be greater than zero or both of them should be less than zero. Therefore, (x – 1) > 0 and (x – 2) > 0 or (x – 1) < 0 and (x – 2) < 0.
Hence, x > 1 and x > 2 or x < 1 and x < 2. If we were to club the ranges, we would get either x > 2 or x < 1. So for any value of x equal to or between 1 and 2, the above equation does not follow.