M4maths Previous Puzzles

03 Mar 2016 Five digit number

The sum of all digits of a 5 digit number is equal to the number of two digit formed by using the ten thousands and hundreds place digit in order. If five digit number has 1, 2, 3, & 4 and no digit is repeated in the number, then total number of possible number are

OPtion

1) 1
2) 6
3) 12
4) 24
5) 36
6) 120
7) 720
8) 1024
9) 1236
10)1500

Solution

Let us suppose that
fifth digit is x
then according to given condition
1+2+3+4+x = y
10+x = y
Since x is a single digit integer
& 0 =< x =< 9
10 =< y =< 19
& repetetion is not allowed
So Possible number are 12x34 where possible x are 0, 5, 6, 7, 8, 9
Ten Thousands digit will necessarily be 1 & hundred x
so order 3 can be arranged in 3! = 6 ways
So possible numbers = 6*6 = 36
Option 5)

Correct Option: 5 Best Solution (10)

Aakash Beniwal   8 years AGO

ans is
Combination of
{'1',2,'0',3,4} .... 6 number
{'1',2,'5',3,4} .... 6 number
{'1',2,'6',3,4} .... 6 number
{'1',2,'7',3,4} ..... 6 number
{'1',2,'8',3,4} ...... 6 number
{'1',2,'9',3,4} .......6 number
so total 36 number

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rayvadera meet    8 years AGO

Sum of 1,2,3,4 is 10. Fifth digit whatever we take sum of digits has last digit equals to fifth digit. Here thousands and hundreds digits should be fixed.So we can place other 3 digits anywhere. for each digit there is 3!=6 possibilities. we can't repeat any digit.therefore there is possibility of 0,5,6,7,8,9 as fifth digit. 6*6=36 possibilites should be the answer.

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vaibhav tiwari   8 years AGO

Maximum sum of the digits can be 19..so ten thousand digit should be 1....unknown value will be taken by hundred digit no..
So...factorial 3 *6 ac hundred digit no. Can take only 0,5,6,7,8,9...digits arenit repeated

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Vaibhav Khedkar   8 years AGO

ten thousands place has to be 1 because sum cannot exceed 19
hundreths place will be filled in 6 ways(0,5,6,7,8,9)
the other three places will be filled in 3! ways
total ways = 3!*6=36
option(5)

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ravi   8 years AGO

the number would be 12_34. Intially the sum of the 4 digits is 10 so without repeating the possible numbers are 0,5-9 so the sum would be from 10-19. So by placing 0 in the _ we get 10=10 and with 5 we get 15=15 so on and the number of combinations for each insertion is 3! so for 6 it becomes 6*3!=36

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ABHINAV PUSHPAM   8 years AGO

The possible numbers are
12543= that can be arranged in 6 ways
12643= that can be arranged in 6 ways

12743= that can be arranged in 6 ways

12843= that can be arranged in 6 ways

12943= that can be arranged in 6 ways

12043= that can be arranged in 6 ways

So in total 36 ways.
Option 5)

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satish ojha   8 years AGO

a+b+c+d+e=10a+c
b+d+e=9a

if a=1 then b+d+e possible 6 case
if a=2. then b+d+e possible 30 case
if a=3,4,5,6,7,8,9 possible 0 case

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Dr.Dipin Singh   8 years AGO

Numbers can be 10XYZ, 15XYZ, 16XYZ, 17XYZ, 18XYZ, 19XYZ
where XYZ are having values 2,3,4 which can be arranged in six (6) ways.
so total possible numbers= 6*6=36... option 5

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MRITUNJAY   8 years AGO

The possible numbers are
12543= that can be arranged in 6 ways
12643= that can be arranged in 6 ways

12743= that can be arranged in 6 ways

12843= that can be arranged in 6 ways

12943= that can be arranged in 6 ways

12043= that can be arranged in 6 ways

So in total 36 ways.
Option 5)

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RAKESH   8 years AGO

at least post the question in proper language.

number ll be of form
1x*xx where, x = 2/3/4 & * = 0/5/6/7/8/9

3! * 6 = 36

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