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4 digit numbers

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by neerajkumar1_1 » Fri Feb 17, 2012 3:24 am
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

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320
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by SARAVANA321 » Fri Feb 17, 2012 3:43 am
neerajkumar1_1 wrote:How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

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320[/quote=4*5*4*4 =320
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by GMATGuruNY » Fri Feb 17, 2012 4:51 am
neerajkumar1_1 wrote:How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

20
150
225
300
320
Good = total - bad.

Total:
The thousands digit must be 2, 4, 6 or 8:
Number of options = 4.
The hundreds digit must be 1, 3, 5, 7, or 9:
Number of options = 5.
The tens digit must be 2, 3, 5, or 7:
Number of options = 4.
The units digit must be 0, 3, 6, or 9:
Number of options = 4.
To combine these options, we multiply:
4*5*4*4 = 320.

Bad:
A bad integer has a thousands digit and a tens digit both equal to 2.
As seen above:
Number of options for the hundreds digit = 5.
Number of options for the units digit = 4.
To combine these options, we multiply:
5*4 = 20.

Good = 320-20 = 300.

The correct answer is D.
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by [email protected] » Fri Feb 17, 2012 7:01 am
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?

20
150
225
300
320


yes just made a silly mistake on this...
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by GMATGuruNY » Fri Feb 17, 2012 6:47 pm
hoyasj wrote:Thanks for the explanation Mitch. Could you please explain why the "bad" to be subtracted out is 5*4. I understand that you have to subtract out the instances where the first and third digits are both 2, but I don't understand why you multiply 5 and 4 to get that.
In a bad number, the thousands digit and the tens digit are both 2.
The other conditions remain in effect: the hundreds digit must be odd; the units digit must be a multiple of 3.

Number of options for the thousands digit = 1. (It must be 2.)
Number of options for the hundreds digit = 5. (1, 3, 5, 7, or 9.)
Number of options for the tens digit = 1. (It must be 2.)
Number of options for the units digit = 4. (0, 3, 6, or 9.)

To combine these options, we multiply:
1*5*1*4 = 20.

In my initial post, I disregarded the thousands digit and the tens digit because there is only 1 option for each of these positions.
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