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How many five-digit numbers?

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by microke » Mon Jun 30, 2008 1:57 am
How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 4 cannot appear more than once in the number?

A 1875
B 2000
C 2375
D 2500
E 3875

Dear Friends, Can any one explain this problem?
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by kanak » Mon Jun 30, 2008 2:32 am
My approach:

Visualize the below empty slots

- - - - -

The first two slots need to be even numbers. The first one can be filled by 4 numbers (2, 4, 6, 8). The second can be filled by 4 numbers (0, 2, 6, 8) i.e., exclude 4 and include 0 in the second spot.

Hence, the first two can be filled up in 4 x 4 = 16 ways.

The remaining three slots have to be filled up using any of 1, 3, 5, 7, 9 digits as they can be repeated. i.e.,

third slot filled by 5 digits
fourth by 5
and fifth by 5

So, 5 x 5 x 5 = 125 ways of filling the last three slots.

Combining, we have 125 x 16 = 2000.

B is the answer.
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by microke » Mon Jun 30, 2008 4:02 am
:D Thanks for the explanation. I misunderstood the left most digit as right-most digits and included zero in the place..But I came across this question in www.youdowetest.com and the answer was C.
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Correct Answer is C

by smarty80in » Mon Jun 30, 2008 7:48 am
The best answer is C.

Not considering the fact that 4 cannot appear more than once, we have a total of 4*5*5*5*5=2500. Now we deduct the possibilities where 4 does appear more than once (in this case it can appear only twice on the two leftmost even digits). In order to do so, we put 4 in the first and second leftmost digits. The rest of the digits are odd: 5*5*5=125.
2500-125=2375
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by debarshi7 » Mon Jun 30, 2008 8:52 am
smarty , are you considering 0 as an even integer while filling up the
second position from the left
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by smarty80in » Mon Jun 30, 2008 9:16 am
yes 0 is an even integer
You can search "Is 0 an even integer" on google and you will get the answer
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by microke » Tue Jul 01, 2008 12:23 am
Thanks smarty80in! You are right...this approach is simple and effective......

and zero is a perfect even number! :wink:
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by Carol » Tue Jul 01, 2008 12:41 pm
smarty80in, I didn't understand why you subtracted 125 from 2500.
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by younggun044 » Tue Jul 01, 2008 4:12 pm
Correct answer is "C".
Smarty approach is absolutely fine. Goodone!!
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by Sunny22uk » Tue Jul 01, 2008 4:57 pm
As per O.G. , 0 is neither a postive integer nor a negative integer.
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by microke » Wed Jul 02, 2008 12:34 am
Then we should follow only GMAC advice....
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by smarty80in » Wed Jul 02, 2008 8:40 am
yes, but still 0 is an even integer

See the page number 108 of OG11
it has given definition and list of even integer
and the OG11 list includes clearly includes 0

Any integer that is divisible by 2 is an even integer, the set of even integers is
{...,-4,-2,0,2,4,6,8,...}


My sincere advice to all you guys, please revise the basics properly.
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by beeparoo » Wed Jul 02, 2008 8:45 am
Sunny22uk wrote:As per O.G. , 0 is neither a postive integer nor a negative integer.
Your comment here is irrelevant. We are not concerned about negative or positive numbers. We are only talking about EVEN or ODD numbers.
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by smarty80in » Wed Jul 02, 2008 9:08 am
subtracted 5*5*5 cases ( in which 4 is coming on 1st and 2nd place) from total number of cases.
We need to subtract because 4 is not allowed more than once and as 4 is an even integer and even integer is allowed only at first 2 places, so 4 can repeat only at first 2 places.
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