Latest Elitmus Aptitude Question SOLUTION: How many five digit numbers can be formed by using the digits 0,1,2,3,4,5 such that the number is divisible by 4?

• Placement Papers
• /
• Elitmus
• /
• Numerical Ability
• /
• Permutation and Combination

Elitmus Question Papers:

(#M40154155) ELITMUS Numerical Ability question Asked on 18-10-2015 Keep an EYE

How many five digit numbers can be formed by using the digits 0,1,2,3,4,5 such that the number is divisible by 4?

Asked In Elitmus Vishal kungwani (8 years ago)

Solved Deepak kumar singh Read Solution (19)

Is this Puzzle helpful?   (28)   (3) Submit Your Solution Permutation and Combination

Read Solution (19) :

Deepak kumar singh  (8 years ago) Best Solution

an s= 144
divisible by 4 means last two digit should always div by 4.
unit place=(04,20,40,12,24,32,52)
_ _ _04
_ _ _ 20
_ _ _40
total no=4x3x2x3=72
_ _ _12
_ _ _24
_ _ _32
_ _ _52
total no=3x3x2x4=72
total n0 = 72+72=144 ans

Is this solution Helpfull? Yes (70) | No (15)  

Nilesh  (8 years ago)

To get a 5 digit no. we must have one of 1,2,3,4,5 in starting---- 5 ways
remaining 2 places can be filled with 0,1,2,3,4,5 ways-----------6*6 ways
A no. to be divisible by 4, last 2 digits must be divisible by 4 -----8 ways (04,,12,20,24,32,40,44,52)


total: 5*6*6*8=1440

Is this solution Helpfull? Yes (14) | No (16)  

Akanksha singh  (8 years ago)

144 is correct answer

Is this solution Helpfull? Yes (7) | No (1)  

ananga  (8 years ago)

168...w/o repitation

Is this solution Helpfull? Yes (7) | No (4)  

guddu kumar  (8 years ago)

if no is divisible by 4 the last two digit(unit and tens place) will be 00,04,12,20,24,32,40,44,52 i.e 9 pairs possible and left most place filled in 5 ways and remaining two places filled in 6 ways each.
so total possible combination=5*6*6*9=1620 (repeatition is allowed).

Is this solution Helpfull? Yes (6) | No (2)  

KISHAN KUMAR  (8 years ago)

144 IS THE 100% RIGHT ANSWER WHICH SOLVED BY DEEPAK

Is this solution Helpfull? Yes (4) | No (3)  

ruparani thunuguntla  (8 years ago)

any number is divisible by 4 means the last two digits should be divisible by 4
so...
possible combinations with the given numbers are 04,12,20,24,32,40,52

case 1: combinations including 0
04,40,20
hence 4*3*2 ways are possible for each combination
hence 4*3*2*3=72 ways
case 2:
12,24,32,52
for these numbers , there are only 3 possible ways to fill first digit place
hence 3*3*2 ways
for 4 numbers
3*3*2*4 =72 ways
hence ans is 144 ways

Is this solution Helpfull? Yes (4) | No (1)  

Rounak Shah  (8 years ago)

Divisible by 4 means last two digit shouldalways div by 4.
Last 2 digit set may be=(04,20,40,12,24,32,52)
case 1=>
_ _ _04
_ _ _ 20
_ _ _40
total no=4x3x2x3=72

case 2 =>
_ _ _12
_ _ _24
_ _ _32
_ _ _52
total no=3x3x2x4=72

total 5 digit no. = 72+72=144 ans

Is this solution Helpfull? Yes (4) | No (1)  

AKHIL KALRA  (8 years ago)

ans is 600

to be divisble by 4 last two digits should be divisble by 4
_ _ _ 20 ->4*5*5(bcoz digits can repeat as per the question) =100
_ _ _40 ->4*5*5=100
_ _ _12 =100
_ _ _52 =100
_ _ _04 =100
_ _ _24 =100

Is this solution Helpfull? Yes (1) | No (4)  

swati  (8 years ago)

ans may be 1620.
1st place 1 to 5 so 5 ways.
2nd place 0 to 5, so 6 place.
3rd place 0 to 5, so 6 place.
4th and 5th place should show that the no is divisible by 4 then 9 ways(00,04,12,20,24,32,40,44,52)

so 5*6*6*9=1620

Is this solution Helpfull? Yes (1) | No (7)  

nishu  (6 years ago)

For the 5-digit integer to be a multiple of 4, the last two digits must form a multiple of 4.
Options:
04, 12, 20, 24, 32, 40, 52.

Case 1: Last 2 digits include 0
Number options for the last 2 digits = 3. (04, 20 or 40.)
Number of options for the ten-thousands place = 4. (Any of the 4 remaining digits.)
Number of options for the thousands place = 3. (Any of the 3 remaining digits.)
Number of options for the hundreds place = 2. (Either of the 2 remaining digits.)
To combine these options, we multiply:
3*4*3*2 = 72.

Case 2: Last 2 digits do NOT include 0
Number options for the last 2 digits = 4. (12, 24, 32, or 52.)
Number of options for the ten-thousands place = 3. (Any of the remaining 4 digits but 0.)
Number of options for the thousands place = 3. (Any of the 3 remaining digits.)
Number of options for the hundreds place = 2. (Either of the 2 remaining digits.)
To combine these options, we multiply:
4*3*3*2 = 72.

Total options = 72+72 = 144.

Is this solution Helpfull? Yes (1) | No   

DEEPMALA TIWARI  (8 years ago)

NOs which ends with 0 24
nos which ends with 2 24
nos which ends with 4 24
total nos 72

Is this solution Helpfull? Yes | No (17)  

phani  (8 years ago)

To get a 5 digit no. we must have one of 1,2,3,4,5 in starting---- 5 ways
A no. to be divisible by 4, last 2 digits must be divisible by 4 -----6 ways (04,,12,20,24,32,40)
remaining 2 places can be filled in 3C2 ways---------------------------6ways

total: 5*6*6=180.

Is this solution Helpfull? Yes | No (7)  

anuj priyadarshi  (8 years ago)

1*3*4*5*1=60 , as at unit place 4 should b fixed and at frst place we cant take zero so nly 1 number. if no. not repeated this will b ansr

Is this solution Helpfull? Yes | No (9)  

DEEPMALA TIWARI  (8 years ago)

for without repeation
A no. to be divisible by 4, last 2 digits must be divisible by 4 -----7 ways (04,,12,20,24,32,40,52)
nos which ends with 04 3*2*1
nos which ends with 40 3*2*1
nos which ends with 12 2*2*1
nos which ends with 24 2*2*1
nos which ends with 52 2*2*1
nos which ends with 20 3*2*1

total nos 34
nos which ends with 04

Is this solution Helpfull? Yes | No (6)  

ujjwal  (8 years ago)

number of number divisible by 4 ending with 0 = 4*3*2*2(2,4) = 48
2 = 4*3*2*3(1,3,5) = 72
4 = 4*3*2*2(2,4) = 48
total number divisible by 4 = 48+ 72+48 = 168(without repeatation)

Is this solution Helpfull? Yes | No (3)  

kumari anjana  (8 years ago)

5*4*3*2*3=360

Is this solution Helpfull? Yes | No (4)  

Chitaranjan kumar  (8 years ago)

126Ans
when unit =0
then ten:2or4
and rest 3 will
3*3*2
total:3*3*2*2:36
now unit:2then ten:1or3or5
so rest:3*3*2
total:3*3*2*3:54
similarly
when unit:4
then total:3*3*2*2:36
Total sum:36+54+36:126

Is this solution Helpfull? Yes | No (3)  

imran alam  (7 years ago)

To get 5 digit no, we can fill first place with 1,2,3,4,5.....5 ways
remaining 2 place can be filled with 0,1,2,3,4,5......6 ways
A no. to be divisible by 4, last 2 digits must be divisible by 4....9 ways (00,04,12,20,24,32,40,44,52)
Total no=9(5x6x6)=1620 ans

Is this solution Helpfull? Yes | No (1)  

Please Login to Read Solution.