Question

A 5 digit number ABCDE made by using 1,2,3,4,5. Its 3 digits ABC is divisible by 4, BCD is divisible by 5 & CDE is divisible by 3, find the value of digit A. ​

Answer 1

Answer:

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Answer 2

Given:

A five digit number ABCDE made by using 1,2,3,4,5

From above number ABC is divisible by 4

BCD is divisible by 5

And CDE is divisible by 3

To find:

We have to find the value of digit A

Solution:

ABC are the first three digits of  number and divisible by 4 also it is formed from the digits 1,2,3,4,5

So let us list out the three digit numbers formed from given digits,They are:

124

132

152

312

324

352

412

512

524

532

Next D digit is 5 in all above numbers because BCD is divisible by 5.Then the nummbers be:

1245

1325

1525

3125

3245

3525

4125

5125

5245

5325

Now from above numbers choose the numbers whose digits are not repeated and then fill the fifth digit with the left over number from 1,2,3,4,5.

Then the final five digit numbers formed will be

12453

13254

31254

32451

41253

Now observe 12453

In this ABC = 124 which is divisible by 4

BCD = 245 which is divisible by 5

CDE = 453 which is divisible by 3

∴ 12453 is the required number which satisfies all the given conditions.

So digit A = 1