Latest TCS Aptitude Question SOLUTION: Find The Sum Of All 4-Digit Numbers, that can be formed from the digits 0,1,3,4,5 without repetition. a)259974 b)337974 c)346632 d)334554

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(#M40003335) TCS Logical Reasoning question Keep an EYE

Find The Sum Of All 4-Digit Numbers, that can be formed from the digits 0,1,3,4,5 without repetition.
a)259974
b)337974
c)346632
d)334554

Asked In TCS Monika Kala (12 years ago)

Solved Dr.Dipin Singh Read Solution (8)

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Read Solution (8) :

tushar  (10 years ago)

it's very simple.
n=5 i.e 0,1,3,4,5
1.for thousandth position we can use only 1,3,4,5.(can not use 0)
add numbers i.e 1+3+4+5=13
thousandth position sum=1000*13*(n-1)!=1000*13*24

2.hundredth position sum=100*13*(n-1)!=100*13*24

3.tenth position sum=10*13*(n-1)=10*13*24

4.unit position sum=1*13*24

5.13*24=312

6.so sum of all 312(1000+100+10+1)
i.e 312*1111
=346632
i.e option c
thank you

Is this solution Helpfull? Yes (19) | No (1)  

Dimple  (12 years ago)

b)337974
Trying to explain sol of DIPIN.
Total 96 numbers can be formed.
No number can start with 0.
no. of numbers starting with 1 or 3 or 4 or 5 = 4*3*2*1=24
when no is starting with 1,
0,3,4,5.. each number will appear in unit place 6 times.
so (0+3+4+5)*6 = 72
when no is starting with 3,
0,3,4,5.. each number will appear in unit place 6 times.
so (0+1+4+5)*6 = 60
when no is starting with 4,
0,3,4,5.. each number will appear in unit place 6 times.
so (0+3+1+5)*6 = 54
when no is starting with 5,
0,3,4,5.. each number will appear in unit place 6 times.
so (0+3+4+1)*6 = 48

sum of digits at unit place of all numbers = 234
sum of digits at tens place of all numbers = 234
sum of digits at hundreds place of all numbers = 234

sum of digits at thousands place of all numbers = 312

adding these values, we get the sum all 4 digit numbers that can be formed from the digits 0,1,3,4,5 without repetition = 3579974.

Is this solution Helpfull? Yes (14) | No (3)  

Dr.Dipin Singh  (12 years ago)

337974

Taking help of solution given by shikha,

Total 96 numbers can be formed.
No number can start with 0.
no. of numbers starting with 1 or 3 or 4 or 5 = 4*3*2*1=24

sum of digits at unit place of all numbers = 234
sum of digits at tens place of all numbers = 234
sum of digits at hundreds place of all numbers = 234

sum of digits at thousands place of all numbers = 312

considering this , sum of all 4 digit numbers that can be formed from the digits 0,1,3,4,5 without repetition = 337974

Is this solution Helpfull? Yes (13) | No (10)  

Suman  (12 years ago)

@ Anup,

I think it is well explained by Dimple and Dipin.

b)337974 should be correct.
Trying to explain sol of DIPIN and Dimple.
Total 96 numbers can be formed.
No number can start with 0.
no. of numbers starting with 1 or 3 or 4 or 5 = 4*3*2*1=24
when no is starting with 1,
0,3,4,5.. each number will appear in unit place 6 times.
so sum of digits at unit place =(0+3+4+5)*6 = 72
when no is starting with 3,
0,1,4,5.. each number will appear in unit place 6 times.
so sum of digits at unit place=(0+1+4+5)*6 = 60
when no is starting with 4,
0,3,1,5.. each number will appear in unit place 6 times.
so sum of digits at unit place=(0+3+1+5)*6 = 54
when no is starting with 5,
0,3,4,1.. each number will appear in unit place 6 times.
sosum of digits at unit place = (0+3+4+1)*6 = 48

sum of digits at unit place of all numbers = 234

Is this solution Helpfull? Yes (4) | No (2)  

Kataria Deepak  (10 years ago)

Simple Formula = n!*(Sum of Given Digits)* (1111 for 4 digit 111 for 3 digit).
for given situation n = 4, sum of digit = 0+1+3+4+5 = 13.
sum = 4! (13) * (1111) = 346634

Is this solution Helpfull? Yes (2) | No   

anup bharti  (12 years ago)

dipin can u explain how this
sum of digits at units palce of all nos=234

Is this solution Helpfull? Yes (1) | No (3)  

Shikha  (12 years ago)

Total 96 numbers can be formed.
No number can start with 0.
no. of numbers starting with 1 or 3 or 4 or 5 = 4*3*2*1=24

sum of digits at unit place of all numbers = 234
sum of digits at tens place of all numbers = 234
sum of digits at hundreds place of all numbers = 234
sum of digits at thousands place of all numbers = 234
sum of digits at ten thousands place of all numbers = 312

considering this , sum of all 4 digit numbers that can be formed from the digits 0,1,3,4,5 without repetition = 3579974

Is this solution Helpfull? Yes | No (4)  

Vinay  (12 years ago)

Dipin please explain

Is this solution Helpfull? Yes | No (2)  

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