moron wrote:I got this question correct but it took too much time and almost about to give up . Reason it took way too much time was I was using kind of trial and error method. All I knew mathemetically these two numbers has to be close to each other and everything onward is trial and error
N and M are 3 digit integers. Each of the numbers 1, 2, 3, 6, 7, and 8 is a digit of either N or M. What is the smallest possible positive difference between N and M?
A) 29
B) 49
C) 58
D) 113
E) 131
To do this most efficiently, you have to see the logic of what you are seeking to do.
The key question here is that of how to make N and M as close to each other as possible. You know that given the digits you need to use N and M will not be the same number. So one will be higher than the other, and within that constraint you want the lower one to be as great as possible and the higher one as small as possible.
You are making three digit integers with hundreds, tens and ones place digits.
You have the digits 1, 2, 3, 6, 7 and 8.
The hundreds place digits make the most difference. So to keep the numbers as close as possible, the hundreds place place digits should be as close as possible. So the hundreds place digits should be separated by a difference of 1.
That gives the following 4 possible pairs. {1, 2} {2, 3} {6, 7} {7, 8}
We want the lower number to be high and the higher one to be low, so let's do our best to save the extreme numbers, 1, 2, 7 and 8 for later, so that we can use them to make the low number high and the high number low.
So choose one of the inner pairs, {2, 3} or {6, 7}, for the hundreds place digits. If the number we come up with is not one of the answer choices or not the lowest answer choice, we can choose the other inner pair and see how that works.
Let's choose {6, 7} So we have 6-- and 7--.
Now make the lower number as high as possible by putting 8 in the 10ths place, and the higher number as low as possible by putting 1 in the 10ths place. 68- and 71-.
Now we have two digits left. Use the greater one, 3, for the lower number and the smaller one 2, for the higher number.
683 and 712
They are 29 apart and the answer is
A.
