Please help me answering this question.A boy forgot his pin code which was of 5 digits but luckily he remembers some hints to remind that password.here are the clues.1 first digit is the square of...

Please help me answering this question.

A boy forgot his pin code which was of 5 digits but luckily he remembers some hints to remind that password.here are the clues.1 first digit is the square of the second digit.2 second plus 3rd digits are equal to 10. 3 4th digit equal to 2nd digit plus 1. 4 5th plus 3rd digit make 14. 5 sum of all five digits makes 30.Whats the code?

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rajatajm's profile pic

rajatajm | Student, Undergraduate | (Level 1) eNoter

Posted on

In the above question the given conditions are:

let 1st digit=a

2nd=b

3rd=c

4th=d

5th=e

1.a=(b)2

2.b+c=10

3.d=b+1

4.e+c=14

5.a+b+c+d+e=30

=> (b)2+b+c+d+e=30     (a=(b)2)

=> (b)2+b+(10-b)+d+e=30    (b+c=10=>c=10-b)

=>  (b)2+b+(10-b)+(b+1)+e=30    (d=b+1)

=>    (b)2+b+(10-b)+(b+1)+(14-(10-b)=30(e+c=14=>e=14-c=>14-(10-b))

=>    (b)2+b+10-b+b+1+14-10+b=30

=>    (b)2+2b+15=30

=>    (b)2+2b=30-15

=>    (b)2+2b-15=0

=>       (b)2+5b-3b-15=0

=>      b(b+5)-3(b+5)+=0

=>      (b+5) (b-3)=0

=>       b+5=0 b-3=0

=>        b= -5 b= 3

so by putting the value of b(2nd digit) in given above equation, we will get

1st digit=9

2nd=3

3rd=7

4th=4

5th=7

 

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

Question:

1 first digit is the square of the second digit.2 second plus 3rd digits are equal to 10. 3 4th digit equal to 2nd digit plus 1. 4 5th plus 3rd digit make 14. 5 sum of all five digits makes 30.Whats the code?

Solution:

Let the format of the 5 difit number be : abcde, where a,b,c,d and e are the digits in the order of a decimal number of 5 digits.

By the given conditions,

a=b^2..............................(1)

b+c=10.............................(2)

d=b+1..............................(3)

c+e=14............................(4)

a+b+c+d+e = 30................(5)

Using (4) and (5)

a+b+d +14 = 30 Or

a+b+d = 30-14 = 16. Using (3) ,

a+b+b+1 = 16 . Or

a+2b = 15. But from (1) a= b^2.

Therefore, b^2+2b = 15  Or b^2+2b-15 = 0 Or (b+5)(b-3) = 0. So b = 3 is the valid value. Therefore, a = b^2 = 3^2 = 9

Therefore  d  =b+1 = 3+1 = 4.

c=10-b =10-3 = 7

a+b+c+d+e =30 Or

9+3+7+4+e = 30 Or e = 7

Therefore,

a=9

b=3

c=7

d=4 and

e =7.

Hope this helps.

 

 

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