pushpitkc hello , can please help me to wrap my mind around Bunuels`s solution

A. all digits are distinct = 3*9*8=216 (first digit can have only three values 7, 8, or 9);


I can not understand why second and third digits are 9 and 8 respectively, any idea?

Hey Dave,


The hundred's digit can be 7 OR 8 OR 9. Thus, there are 3 ways to fill the first place.

While filling the hundred's place, we will have only 9 options with us. The reason that we have 9 options with us is because ALL the digits of the number are distinct. And we have already used one of the number in the hundreds place.

Think about it. Once we put the digit 7 in the hundred's place, we can put 0 OR 1 OR 2 OR 3 OR 4 OR 5 OR 6 OR 8 OR 9 (9 options) in the tens place.

Now suppose you have place 1 in the tens place. So you have used 7 and 1 in the two places, thus, you will be left with 8 options for the units place( 0 OR 2 OR 3 OR 4 OR 5 OR 6 OR 8 OR 9)

Thus, that is the reason, we are writing all the possible cases as 3 x 9 x 8 (3 possible cases for the hundreds place, 9 possible cases for the tens place and 8 possible cases for the units place)

I hope this clears your doubt.

Regards,
Saquib
e-GMAT
_________________

We don't even have to solve this question. Just use the logic!!

Because of the symmetry, 3 digit integers that have two digits that are equal to each other and the remaining digit different from the other two from 700-799 is equal to that are from 800-899 or 900-999

Hence total 3 digit numbers greater than 700 have two digits that are equal to each other and the remaining digit different from the other two
= 3k-1 (as we have to exclude 700)

Only option C is in the form of 3k-1

Hi can someone help me understand why the following line of reasoning does not give an answer that matches

7 _ _ : two possibilities: digit 2 is 7 and digit 3 can be from zero to 9 except 7 or digit 2 is any number from 0 to 9 except 0 and 7 and digit 3 is the same : this implies

Possibility 1: 1*9 = 9
Possibility 2: 8*1 =8
Total = 17

simillar reasoning for 8 and 9 so 17*3 = 51

Quick alternative: You know that the answer has to be 1 less than a multiple of 3 (since there are 3 ranges of numbers and the number of eligible values in the 700 range is equal to the number of eligible values in the 800 and 900 range, minus the value 700 itself).

C