rakeshd347 wrote:Please explain the best way to solve this.

lunarpower wrote:There's an insight here that solves the problem immediately, given these answer choices. Here it is: You're given a SUM. If you switch digits in the same decimal place, the sum is unchanged.

For instance, if you have xxxxx7 + yyyyy5, then that's the same as xxxxx5 + yyyyy7. And so on with the tens digits.

Why would we care?
Well...
You know there's at least one solution.
But, as soon as there's one solution:
* You can switch the units digits (--> another solution).
* You can switch the tens digits (--> another solution).
* You can switch the tens digts AND switch the units digits (--> another solution).

You know these are all different solutions, because no digit appears more than once. Furthermore, given any solution, you could always do the same thing.
So, solutions are going to appear in groups of four.

The only multiple of four here is 4. Done.

--

If you don't have the above insight, then just start listing out possibilities, as the posters have done nicely above.

lunarpower wrote:
My brain doesn't really understand things unless they are simple. On this test, that's a huge advantage.

lunarpower wrote:
I use analogies because the human brain is fundamentally wired for analogies/examples/experience, and not for rules.

Think about how you learn your first language, of which your knowledge is incredibly thorough. (Even if a professional linguist studies your language for years and years, (s)he will not approach anywhere near the level of competency you had in it when you were 11-12 yearsold.)
How many "rules" for your first language do you learn growing up? Zero. None. Just endless exposure to tons and tons of examples (from your parents, your friends, and whomever else).

Growing up, even if you see something stated in the form of a rule, you'll understand it not as a rule, but by connecting it to examples that already exist in your head.
For instance, when sixth-graders learn that "singular subjects need singular verbs", that rule is incomprehensible by itself. But, once kids realize that the rule is just fancy language for the fact that "My dog has fleas" is right and "My dogs has fleas" is wrong, then it instantly makes sense.

In fact, the labels "singular" and "plural" aren't at all necessary, unless you are trying to communicate grammatical ideas to other people. In terms of understanding how the grammatical system works, they are irrelevant, and may even inhibit understanding rather than promote it.