If the seven-digit number 49x29y6 is divisible by 72, then what will be the value of (x+2y) for the largest value of x and y?

For the number to be divisible by 72, it must be divisible by 8 and 9.
1. Divisibility by 8:
The last three digits 9y6 must be divisible by 8.
Let's check values from y=9 downwards:

If y=9: 996÷8=124.5 (No)

If y=8: 986÷8=123.25 (No)

If y=7: 976÷8=122 (Yes)

If y=3: 936÷8=117 (Yes)

Since we want the largest possible values, we choose y=7.

2. Divisibility by 9:
The sum of all digits must be divisible by 9.

Sum=4+9+x+2+9+y+6=30+x+y
Substitute y=7:

Sum=30+x+7=37+x
For 37+x to be divisible by 9, x must be 8 (since 45 is the next multiple).

3. Evaluate (x+2y):

x+2y=8+2(7)=8+14=22