Find the sum of all five digit number that can be formed using the digits 1,2,3,4 and 5 (repetition of digits not allowed)
sheelanadh,
Always post the answer options for the PS question.
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help me to solve it
Source: Beat The GMAT — Problem Solving |
Find the sum of all five digit number that can be formed using the digits 1,2,3,4 and 5 (repetition of digits not allowed)selango wrote:sheelanadh,
Always post the answer options for the PS question.
a)3999960.
b)5273222.
c)3777660.
d)3998900.
please help me to solve it........
this is not too hard but very time-consuming
from digits 1,2,3,4,5 using digits only once we can form 5!=120 numbers
when we sum all numbers each digit in all numbers will appear exactly 120/5=24 times
1*24+2*24+3*24+4*24+5*24=360
and now let us sum
12345
12354
12543
..........
..........
..........
.....360
...360
..360
..........
the right answer to me 39999960-A
from digits 1,2,3,4,5 using digits only once we can form 5!=120 numbers
when we sum all numbers each digit in all numbers will appear exactly 120/5=24 times
1*24+2*24+3*24+4*24+5*24=360
and now let us sum
12345
12354
12543
..........
..........
..........
.....360
...360
..360
..........
the right answer to me 39999960-A
thank you very much .... can you explain me in simple method..clock60 wrote:this is not too hard but very time-consuming
from digits 1,2,3,4,5 using digits only once we can form 5!=120 numbers
when we sum all numbers each digit in all numbers will appear exactly 120/5=24 times
1*24+2*24+3*24+4*24+5*24=360
and now let us sum
12345
12354
12543
..........
..........
..........
.....360
...360
..360
..........
the right answer to me 39999960-A
i will try with simple example
imagine that you have the same task but with digit 1,2,3
with this you have 3!=6 numbers
123
132
213
231
312
321
and now sum them
as you notice all digits (1,2,3) appear 6/3=2 times
start to sum units
(1+1)+(2+2)+(3+3)=12 and 2 will be the unit digit of the answer.
the sum of the tenths will be exactly the same -12+1(from units)=13,
the same for hundreds and the resulting answer
1332
imagine that you have the same task but with digit 1,2,3
with this you have 3!=6 numbers
123
132
213
231
312
321
and now sum them
as you notice all digits (1,2,3) appear 6/3=2 times
start to sum units
(1+1)+(2+2)+(3+3)=12 and 2 will be the unit digit of the answer.
the sum of the tenths will be exactly the same -12+1(from units)=13,
the same for hundreds and the resulting answer
1332
