Answer: B
The best approach for this question is to make them somehow seem look like each other and write them in form of multiplication thus we can simplify them easily.
Here the minimum multiply factor of both can be 10^4 :

A: 10^6 + 10^5 = 10^4 * (10^2 + 10^1)
B: 10^7 + 10^4 = 10^4 * (10^3+ 1)

10^4 is the same between both of them, so we compare (10^2 + 10^1)=110 and (10^3+ 1)=1001 which (10^3+ 1) is bigger and B is bigger than A

If you realize that $10^7$ is 10 times $10^6$, you will immediately choose the quantity with $10^7$.

$10^7=10*10^6=10^6+10^6+10^6+10^6+10^6+10^6+10^6+10^6+10^6+10^6$, thi swill surely be greater than $10^6+10^5$
so B>A

Be careful! These quantities are not equal! When multiplying exponents with the
same base, it is correct to add the exponents:
106 × 105 = 1011
However, numbers raised to powers cannot be directly combined by addition or
subtraction. Instead, sum this way:
Quantity A = 106 + 105 = 1,000,000 + 100,000 = 1,100,000
Quantity B = 107 + 104 = 10,000,000 + 10,000 = 10,010,000
Thus, Quantity B is greater.

This is the best way, IMO.

I would probably use one of the approaches already offered.
That said, below is an alternate approach that might be useful in other problems.

Test an ANALOGOUS case with smaller values.
If we reduce every exponent by 4:
Instead of $10^6+10^5$, Quantity A = $10^2 + 10^1 = 101$
Instead of $10^7+10^4$, Quantity B = $10^3 + 10^0 = 1001$
Quantity B is greater.

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