∴

*e *can take any value from 11 to 19.

The product of both the terms is 9.

∴ Their sum would be minimum when they will be equal.

We would consider only positive value of

*x*, ∵

*x* > 0.

Similarly for

*d *we get,

*d* = 25 − |7 +

*y*|

As

*d *is positive integer, the minimum value

*d *can have is 1 and as modulus is always positive hence the maximum value of

*d* can be 25.

∴

*d *can take any value from 1 to 25.

So as the minimum value of

*a* is 6, maximum value of

*d *is 25 and range of

*e* is from 11 to 19 then we will have to reconsider the range of value of the numbers so that all the conditions hold true.

As minimum value of

*d *is 1, it cannot be less than

*e *and

* b*,

*b* is greater and minimum value of

*e *is

* *11.

∴ Minimum value of

*b *is 12 and that of

*d *is 13.

Maximum value of

*d *is 25 hence maximum value of

*b *is 24.

Similarly,

As

*a *has to be smaller than

*c *and

*e,* maximum value of

*e *is 19 and

*c* is smaller than

*e*.

∴ Maximum value of

*c* is 18 and that of

*a *is 17.

Minimum value of

*a *is 6 and hence minimum value of

*c *is 7.

∴ Finally, we get,

6 ≤

*a* ≤ 17

7 ≤

*c* ≤ 18

11 ≤

*e* ≤ 19

12 ≤

*b* ≤ 24

13 ≤

*d* ≤ 25

∴ The range of values of

*p *is:

∴ The range of the sum is [49, 103].

Hence, option 5.