Question

What is the sum of all the integral values of ‘x’ that satisfy the inequality 0 < x (x + 1) (x + 3) (x + 4) < 210.
1. 9
2. 10
3. -9
4. -10

Answer 1

Correct Answer - Option 4 : -10

Calculation:

The value of the expression x (x + 1) (x + 3) (x + 4) is positive for x > 0, negative for -1 < x < 0, positive for -3 < x < -1, negative for -4 < x < -3 and positive for x < -4

For x = -5, the value is -5 × -4 × -2 × -1 = 40

For x = -6, the value is -6 × -5 × -3 × -2 = 180

For x = -7, the value is -7 × -6 × -4 × -3 = 504

For x = -2, the value is -2 × -1 × 1 × 2 = 4

For x = 1, the value is 1 × 2 × 4 × 5 = 40

For x = 2, the value is 2 × 3 × 5 × 6 = 180

For x = 3, the value is 3 × 4 × 6 × 7 = 504

So, the values of ‘x’ which satisfy the inequality are -6, -5, -2, 1 and 2.

The sum of the values is -10.