Previous Year Questions

Given: a > b

From statement I: (8⁶ * 4^{2 + a})/(16^-2b * 2^4a) = 64^{3(2a - 4)}

2¹⁸ * 2^{2(2 + a)} * 2^8b * 2^-4a = 2^{18(2a - 4)}

Then, 18 + 2(2 + a) + 8b - 4a = 18(2a - 4)

18 + 4 + 2a + 8b - 4a = 36a - 72

19a - 4b = 47

From statement II: Difference between a and b is 2 and, 2(a + 3b - 9) + 4a = 6(b - 3 + a).

a = 2 + b

And, 2(a + 3b - 9) + 4a = 6(b - 3 + a)

2a + 6b - 18 + 4a = 6b - 18 + 6a

So, this equation is invalid as both sides are equal and also the value becomes zero.

From statement I and II:

19(2 + b) - 4b = 47

38 + 19b - 4b = 47

b = 3/5

Then, a = 2 + 3/5 = 13/5

Hence, both statements I and II together are sufficient.