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Cryptarithmetic Problem 1

Cryptarithmetic_Problem_1

1.  Value of A ?
(a) 5 (b) 6 (c) 7 (d) 9
2. Value of R + P + A + D ? 
(a) 20 (b) 21 (c) 23 (d) 24
3. Value of P ?
(a) 6 (b) 7 (c) 8 (d) 9

Video Solution

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16 comments

  1. surabhi

    I googled so much to find a proper elitmus pattern and other information related to it,but no where i was able to find something so informative and proper like this.Commendable work!!
    Thanks a lot

    1. ElitmusZone Post author
      (For explanation only)
      Let's take P=0
      
                       A  0  D
                       x  A  D
                    R  0  A  D
                 D  D  C  D   
                 D  0  C  E  D 
      If you will take P=0, then Value of R + D =_0 (10)
      So, the carry will be 1. But in the next addition (highlighted in red color). Value of D is present without addition of carry (1). 
      [ i.e. D + 1= _x(Expected value after taking P=0)(x may take any values]
      
      
                       A  9  D
                       x  A  D
                    R  9  A  D
                 D  D  C  D   
                 D  9  C  E  D
      
      
      So, you cannot take value of P=0. It will not satisfy the whole problem.
      If you  start solving the problem after taking P=0, at some stage value of P=0 will be rejected.
      
      Please go through the Cryptarithmetic tutorial. 
    2. Ranjani Kumari

      Because P+C=C, so this possible only when P ={0,9}. If we take P=0, multiplying anything with p i.e, 0 will give P. which is not coming as true here. so p=9. And for why A not equal to 1. because if A-1, when multiplied by A P D it should give same A P D which is not true here.

      1. Ranjani Kumari

        Because P+C=C, so this possible only when P ={0,9}. If we take P=0, what happens explanation is given. So, P=9. And for why A not equal to 1, because if A-1, when multiplied by A P D it should give same A P D which is not true here.

  2. Kunubal Kant

    Start Analysing from D , as it is the only letter here Which should be either 5 or 6.

    Because when D should be multiplied by D itself then the Units place of the new no. should be D only. And this is only possible if ,
    D={5,6}

    However the correct value of D is 5 .

      1. Kunubal Kant

        Dear Karhik,

        Yes D can be 1.

        But assuming D=1 will not give you the solutions(Why ?)
        Because if D=1 then Cryptarithmetic Problem will be so much easier to solve, which you should never expect from elitmus.

        So, whenever these situation comes D*D=D(unit place) , then better to try first with D={5,6}

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