Question

How many positive integer values can x take that satisfy the inequality (x - 6)(x - 8)(x - 10) ........ (x - 100) < 0?

• A. 24
• B. 20
• C. 48
• D. 72

Answer 1

The correct option is A 24

Positive integer values ----> (0, infinity)
Total there are 48 terms.
[101, infinity) ------> product will be positive.
[1, 5] -------> product will be positive.
[6, 8, 10.......100] ------>result zero.
when x = 7,
One positive term and 47 negative terms. So, the product will be negative.
when x = 9,
Two positive terms and 46 negative terms. So, the product will be positive.
.
.
.
and so on.
7, 11, 15, ....... 99 satisfies the given inequality.
Therefore, x can take 24 values.