How many 3 digits even numbers are possible using the digits 0, 3, 1

Hi,
Is it implicit that if were not told the phrase "pick numbers without repetition", We would assume that we can repeat the numbers for units, tents and hundreds digits?

Hey rodrigo.mendozay,

Thanks for pointing this in question.

We have updated the question

Hi,

As per my understanding

Answer should be 36

Case 1
0 at unit digit 5*4 ways
6 at unit digit 4*4 ways

Total 36

Can you tell me where I went wrong??

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Hi. I am a bit confused. Let's say if 0 or 6 is picked for the unit digit, there should be left with only 5 options on the tens digit and 4 options for the hundreds digit right? since all digits have to be different.
can someone please help?

Hi,
If you set "without repetition" so the answer will change to 36 ways. The guy above is right.

I agree with Slomo5000 .

I think the answer is 36.

Hello Payal,

If the unit's place includes '0', the tenth place cannot include '0' as the question states the numbers cannot repeat. You've considered '0' for both tenth place and ones place in your solution.

I used the below approach and I'm getting a different answer, please let me know where I'm going wrong.

Last digit is 0
Tens place and hundredth place - 5x4 =20 ways.

Last digit is 6.
Tens placeand hundredth place - 4x4 = 16 ways.

So a total of 36 ways.

Cheers!

For a 3 digit number to be even, it has to be either 0 or 6.

Constraint: all digits have to be different

Case 1: With 0 as the last digit.

Units digit = 0 --> 1 way
Tens digit can be 3,1,6,7,9, and NOT 0 --> 5 ways
Hundreds digit cannot be 0 and tens digit --> 4 ways
Total = 1 x 5 x 4 = 20 ways

Case 2: With 6 as the last digit

Units digit = 6 --> 1 way
Tens digit cannot be 6 --> 5 ways
Hundreds digit cannot be units digit, tens digit, and zero --> 3 ways
Total = 1 x 5 x 3 = 15 ways

Total = case 1 + case 2 = 20 + 15 = 35 ways.

Could someone please tell me where I went wrong? Thank you!

Hey Slomo,

There is nothing wrong with your method. There was just some confusion while updating the question stem. Apologies for that.

If repetition is not allowed then in that case the total cases will definitely be 36.

When 0 is at the units place then the tens and hundreds digits can be filled in 5 x 4 ways.

However, when 6 is at the units place, then the hundreds place can be filled in only 4 ways and even the tens place can be filled in 4 ways.

Thus, total cases possible will be 20 + 16 = 36 ways.


Regards,
Saquib
Quant Expert
e-GMAT

Hey Wildflower,

I have highlighted the areas where you made a mistake.

Whenever you have a situation in which 0 is involved, try to fill that space first, where the confusion will happen (hundreds place in this case)!

When 6 has been placed in the units digit, we are left with the following options for tens and hundreds place: 0, 1, 3, 7 and 9

Now, if you fill the tens place first and say that there are five ways to fill it, then you are basically saying that I can put 0 in the hundreds place, I can put 1 also, I can put 3 or 7 or 9 also in the hundreds place.

Now think a bit. If you put 6 in the units place and say 0 in the tens place, how many digits are available for the hundreds place? We have 3,7,9 and 1 available right?

However, you have written that the hundreds place can be filled in only 3 ways, which is incorrect!

So, I hope you understand what cases you are missing out?

You are missing those cases, when 0 is put on the tens place.

Thus, to avoid such confusion, what we do is that we fill the hundreds place first and say that the hundreds place can be filled in 4 ways (1,3,7 or 9), this ensure that all eligible digits will get a chance to be placed at the hundreds place.

Now with are left with 0 and the remaining 3 digits (since one of the digits is already placed at the hundreds place), thus total available cases for the tens place will also be 4 and thus the correct answer will be 4 x 4 = 16.


Let me know if you still have any doubts.


Regards,
Saquib
Quant Expert
e-GMAT

Hey,

I have updated the question. Please check.

If repetition is allowed then 60 cases are possible. If it is not allowed then 36 cases are possible.


Regards,
Saquib
Quant Expert
e-GMAT

I see where I went wrong. Thank you, EgmatQuantExpert for pointing it out

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