Let a, b, c, d be four single digit positive integers such that a + b = 11, b + c = 9. If ab > bc > cd, then a = ?

Given that a + b = 11 and b + c = 9, we can infer that a, b, c are all single digit positive integers.

Step 1: Since a + b = 11 and both a and b are single digit integers, the possible pairs (a, b) are (2, 9), (3, 8), (4, 7), (5, 6).

Step 2: Similarly, since b + c = 9, the possible pairs (b, c) are (1, 8), (2, 7), (3, 6), (4, 5).

Step 3: The common 'b' in both equations is 2. So, the pairs become (a, b) = (9, 2) and (b, c) = (2, 7).

Step 4: Now, we are given that ab > bc > cd. Substituting the values of a, b, c we get 92 > 27. This is true as 18 > 14.

Step 5: We don't know the value of 'd' but we know that 'cd' should be less than 'bc'. Since 'c' is 7, for 'cd' to be less than 'bc', 'd' has to be less than 2. But 'd' is a positive integer, so the only value 'd' can take is 1.

So, a = 9.