Question

A 5 digit number abcde is made by using 1,2,3,4,5,. Its three digit abc is divisible by 4, bcd is divisible by 5 and cde is divisible by 3. Find the value of a. Each digit is used once.​

Answer 1

Answer:

Value of a = 1 (Option C)

Step-by-step explanation:

Dude thank you for posting this question, I was feeling sleepy but this question seemed so interesting that I completely focused on solving it and now I'm again feeling like an owl xD

So,this question can be done in multiple ways,one the shorter one and the other the very conceptual one and honestly shorter way isn't really short xD so better if I provide the conceptual way of doing this question. So let's start *drum_roll*

Here according to the question we are required to know the test for divisiblity by 3,4 and 5. And that's all you require to solve this question.

As mentioned we have 5 digit number abcde formed using the digits 1,2,3,4 and 5 and also given that :

• abc is divisible by 4

Test for divisibility by 4 :

• Divide the last two digits by 4 and if they are completely divisible then the number is said to be divisible by 4.

Here we can only have few numbers which are divisible by 4 because we have been given a range of digits. So,the numbers possible are :

• 12,24,32

Condition 2 :

• bcd is divisible by 5.

Test for divisibility by 5 :

• If the units digit of any number is 5 or 0 then the number is divisible by 5. Here based on the range we don't really need to care about 0 (it's literally performing the role of "zero" here xD)

So, bcd has d as it's units digit,so we have figured out the value of one letter at least i.e d = 5.

Condition 3 :

• cde is divisible by 3.

Teet for divisibility by 3 :

• If the sum of digits of the number is divisible by 3, then the number is divisible by 3.

We already know the value of d and also we already formed the only possible numbers which are divisible by 4,so we can plug in these values and check if the sum of the digits is divisible by 3 or not. Let's first check, then we can understand it better.

So,in cde we already know that d = 5. We have only c and e.

Case 1 :

In a b c d e now let's try by hit and trial to figure out which number divisible by 4 (12,24,32) and those digits given in the question (1,2,3,4,5) help us form a number whose sum will be a number divisible by 3.

=> a b c d e

=> a 1 2 5 3 (try putting e =3,we just trying our best xD)

The sum of 2 + 5 + 3 = 10, which is not divisible by 3.

So, let's try other combination,

=> a b c d e

=> a 1 2 5 4 (here e = 4,of course assumed)

Sum of 2 + 5 + 4 = 11, which is again not divisible by 3.

Moving onto other possibilities,now we will try with 24 because no more choices left with 12.

=> a 2 4 5 3 (here e = 3, assumed again!)

Sum of 4 + 5 + 3 = 12, which is divisible by 3.

So,the only digit left is 1, therefore value of a = 1.

And the 5 digit number is 12453.

The short trick is : Do the calculation in head and remember the divisibility tests xD you can try on your own, start with fixing the value of d and then divide the digits by the number mentioned in the question, this will actually strike out all the possibilities quickly and you will be left with only number, which will be value of a.