mandvi19

\(a\) and \(b\) are positive integers.

Given we want the biggest possible value of K, let’s go by options, and start with the biggest value

In options, we can check combination of factors as a case each


Example

For k = 74
74 = 37 x 2
In 5a + 7b, the end unit level should be 4. 5a will always end in 5 or 0.
Now if we consider these as cases,
Case 1 - 5a ends with 0
- then for 7b ends with 4 at 14 (7x2). In such a case the largest k value possible is 5x8 + 7x2 = 40 + 14 = 64. So not satisfied.
Case 2 - 5a end with 5
- then we need 7b to end in -1 or +9.
Since a = +ve, so -1 is ruled out.
7b ends with 9 at 49 (7x7). In such a case the largest k value possible is
5X1 + 7X7 = 5 + 49 = 54. So not satisfied.
5X3 + 7X7 = 15 + 49 = 64. So not satisfied.
5x5 + 7x7 = 25 + 49 = 94. So not satisfied.


For k = 70

70 = 14 x 5

Case 1
5a + 7b = 5 x7 + 7x 5 = 70 —-> so a=7, and b = 5, give k = 70. Which is the largest possible k value