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We make 4 digit codes and each digit of the code form from 1, 2, 3, an

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We make 4 digit codes and each digit of the code form from 1, 2, 3, an [#permalink]

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We make 4 digit codes and each digit of the code form from 1, 2, 3, and 4. If none of each digit use more than once, eg, 1234 can be a code but 1124 cannot be a code, what is the sum of all the possible codes?

A. 56,660
B. 58,660
C. 60,660
D. 66,660
E. 68,660


* A solution will be posted in two days.
[Reveal] Spoiler: OA

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Re: We make 4 digit codes and each digit of the code form from 1, 2, 3, an [#permalink]

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MathRevolution wrote:
We make 4 digit codes and each digit of the code form from 1, 2, 3, and 4. If none of each digit use more than once, eg, 1234 can be a code but 1124 cannot be a code, what is the sum of all the possible codes?

A. 56,660
B. 58,660
C. 60,660
D. 66,660
E. 68,660


* A solution will be posted in two days.


Hi,

its a 4 digit code from four different digits..
so each digit will come equal number of times in each digits place when all codes are attached.

so in thousnds place, hundreds place, tens and units place, the sum would be = (1+2+3+4)*x..
x is what we have to find ...
lets see how many times 1 will be in thousands place..
when thousands is taken by 1, the remaining three places can be occupied in 3! ways.. 6 ways..

so the number becomes=..
th....h....tens....units
60..60...60.......60....
so when we carry over the numbers..
units digit=0
tens=60+6, so tens digit=6
hundreds=60+6, so hundreds digit=6
thousands=60+6=66...
our sum=66660...
D

2) the sum has to be div by 11and 6,
as each number 1,2,3,4 is used equal number of times at four places..
only 66660 fits in
D
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Re: We make 4 digit codes and each digit of the code form from 1, 2, 3, an [#permalink]

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MathRevolution wrote:
We make 4 digit codes and each digit of the code form from 1, 2, 3, and 4. If none of each digit use more than once, eg, 1234 can be a code but 1124 cannot be a code, what is the sum of all the possible codes?

A. 56,660
B. 58,660
C. 60,660
D. 66,660
E. 68,660


* A solution will be posted in two days.


Total Numbers that can be made by using digits 1,2,3,4 without repetition of any digit in a number = 4*3*2*1 = 4! = 24

Now Since every digit has equal chances to appear at any place out of 4 places so each digit will be used at each of the four places an equal number of times

i.e. each digit will be used at Unit digit = 24/4 = 6 times

i.e. 6 numbers will have 1 as unit digit, 6 numbers will have 2 as unit digit, 6 numbers will have 3 as unit digit and 6 numbers will have 4 as unit digit

i.e. Sum of Unit digits of the numbers = 6*(1+2+3+4) = 60

i.e. Number will be _ _ _ 0 with 6 as carry over on ten's place

Now sum of the tens digit will again be 60 and adding carry over will make it 66

i.e. Number will be _ _ 6 0 with 6 as carry over on Hundred's place

Now sum of the Hundreds digit will again be 60 and adding carry over will make it 66

i.e. Number will be _ 6 6 0 with 6 as carry over on Thousand's place

Now sum of the Thousand's digits will again be 60 and adding carry over will make it 66

i.e. Number will be 66 6 6 0

Answer: Option D
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Re: We make 4 digit codes and each digit of the code form from 1, 2, 3, an [#permalink]

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We make 4 digit codes and each digit of the code form from 1, 2, 3, and 4. If none of each digit use more than once, eg, 1234 can be a code but 1124 cannot be a code, what is the sum of all the possible codes?

A. 56,660 B. 58,660 C. 60,660 D. 66,660 E. 68,660

--> (1,000*6+2,000*6+3,000*6+4,000*6)+(100*6+200*6+300*6+400*6)
+(10*6+20*6+30*6+40*6)+(1*6+2*6+3*6+4*6)
=10,000*6+1,000*6+100*6+10*6
=66,660

Therefore, the answer is D.
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Re: We make 4 digit codes and each digit of the code form from 1, 2, 3, an [#permalink]

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New post 21 Jun 2017, 01:46
Numbers to be used: 1 , 2 , 3 , 4
total number of possibilites= 4 . 3 . 2 . 1 = 24 (no repetition of any number)
We need to calculate sum of these 24 combinations of numbers.

Since there are 4 numbers (1,2,3,4) and 24 combinations of numbers, then each number will be used 24/4 =6 times in the total sum.
xxxx
yyyy (x+y+z) = 6 x 4 + 6 x 3 + 6 x 2 + 6 x 1 = 60
+zzzz at units place = 0 (6 will be carried)
at tens place = 0+6 = 6 ( 6 is from previous carry, and 6 again will be carried)
at 100s place = 6 with 6 carried forward
at 1000s place =6 with 6 carried forward
at 10,000s place = 6 from previous carry

ANS = 66660

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Re: We make 4 digit codes and each digit of the code form from 1, 2, 3, an [#permalink]

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New post 05 Sep 2017, 09:20
I feel it is a very tough question that cannot be solved within 2 min.
Has it appeared on the GMAT or is it that only I am finding it difficult.
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Re: We make 4 digit codes and each digit of the code form from 1, 2, 3, an [#permalink]

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New post 08 Sep 2017, 05:20
souvonik2k wrote:
I feel it is a very tough question that cannot be solved within 2 min.
Has it appeared on the GMAT or is it that only I am finding it difficult.


formula =1111*sum(a+b+c+d)*n-1! (in this case n-3)

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Re: We make 4 digit codes and each digit of the code form from 1, 2, 3, an   [#permalink] 08 Sep 2017, 05:20
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