A student is forming numbers without repetition from the digits 1, 2,

can you explain how and when we use the half rule?

KarishmaB Can you please explain this "half rule" ? MartyMurray

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­We can think about this situation logically.

The student is creating all possible five-digit numbers with the digits 1, 2, 3, 4, and 5.

Of course, in some cases, the units digit will be greater than the tens digit. So, the question become, in what proportion of the cases?

Notice that the same digits can appear in the units digit and tens digit positions. For example, we could have 23451 and 23415. In other words, there's no difference between what can be a units digit and what can be a tens digit. Thus, in the cases of all possible such numbers, any given digit will appear equally as often in the tens digit position as in the units digit position.

Accordingly, the number of numbers such that the units digit is greater than the tens digit must be equal to the number of numbers such that the tens digit is greater than the units digit.

Thus, of all possible values, half would have a greater units digit.

What's more important than understanding all that is understanding that you could have figured that out yourself. There's no "half rule." All that's going on is that logic dictates that half the cases will satisfy the given criterion, and a great way to prepare for the GMAT is to reason through things like that so that when you have an opportunity to use logic to quickly find an answer when you take the test, you have practice in doing so.

­Where in the question is it written that the number should be a 5 digit number. We can also solve it for each case considering : 2 digit, 3 digit , 4 digit & 5 digit numbers

It's not explicitly written as such but the answer choices logically point to 5 digits

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