HOW TO RECALL FORGOTTEN PIN OF ATM CARD A REASONING QUESTION
Solve this Mathematics problem in 5 minutes
A house wife forgot her 'ATM PIN' which is a four digit number, but luckily she remembers some hints on how to recall this 'PIN'
Here are some of the clues
1. The 1st digit is half of the 2nd
2. The sum of the 2nd and 3rd digits is 10
3. The 4th is equal to the 2nd plus 1
4. The sum of all digits is 23
What is her ATM PIN?
Solution
Let the four digits PIN be wxyz, Here 1st ,2nd .3rd and 4th digit are w,x,y and z respectively .
According to 1st condition
w = x/2 ............................. (1)
2nd condition
The sum of the 2nd and 3rd is 10 i.ex + y = 10
This implies y = 10 - x .................... ( 2 )
3rd condition
The 4th is equal to the 2nd plus 1 i . e
z = x + 1 .......................... ( 3 )
According to 4th condition
The sum of all digits is 23 . i e .
w + x + y + z = 23 ............ ( 4 )
How to find 2nd digit
1st of all we have to find the value of x .because x is related to all other equations.
Putting the values of w ( from eq1) , y (from eq 2), z( from eq3) in ( 4) we get
x/2 + x + 10 - x + x + 1 = 23,cancelling 'x'
3x/2 +11 = 233x/2 =23-11
3x/2 = 12
x = 8 , This is our 2nd digit
Now put the value of x in (1)
w = 8/2
w = 4 , This is our 1st digit
To find 3rd digit Put the value of x in (3)
z = x + 1
z = 8 + 1
z = 9, This is our 4th digit
To find 3rd digit Put the value of x in (2)
y = 10 - 8
y = 2 , This is our 3rd digit
So The PIN Would be wxyz ➡️4829
Verification
1 The 1st digit is half of the 2nd ➡️ 4 and 8 , definitely 4 is half of 8
2. The sum of the 2nd and 3rd is 10 ➡️ 8+2 =10
3. The 4th is equal to the 2nd plus 1 ➡️ 9 = 8+1
4. The sum of all digits is 23 ➡️ 4 + 8 + 2 + 9 = 23
Conclusion
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