Find digit P in multiplication 7P5 × 33 = PPPP + PPPP

[rajesh]

P corresponds to prime digits(i donno what thi means...i am giving exactly as given in a test)

7P5
x33
---------
PPPP
PPPP
----------
PPPPP


Find the value of P?

 

[Rogerio]

P corresponds to prime digits(i donno what thi means...i am giving exactly as given in a test)

7P5
x33
---------
PPPP
PPPP
----------
PPPPP


Find the value of P?

Let's suppose P is a string of digits.
From 5x3 -> P ends in a '5'
From PPPP+PPPP = PPPPP -> P ends in a '0'

So it's impossible.

 

[rajesh]

actually i could not put the correct indentation(i am new to this site)...

somebody tell me how to attach a file

 

[Gokul43201]

Is this what you want ?

             7 P 5
             x 3 3
         ---------
           P P P P             
         P P P P
        ----------
         P P P P P

 

[Gokul43201]

Even with the indentation (enclose within [ code] [ /code] tags), there would be no solution, as you would have PPPP + PPPP0 = PPPPP.

Why is this impossible ?

PPPP -> 1000P+100P+10P+P = 1111P and similarly PPPP0 ->11110P, so adding should give 12221P, but clearly PPPPP -> 11111P, a contradiction, unless P=0. But clearly P can't be 0.

 

[Gokul43201]

I think you haven't copied the problem down correctly...

Here's another reason why this is wrong (if you're not happy with the previous ones) :

700 X 33 = 23100
800 X 33 = 26400

So clearly 7P5 X 33 must be in the 2 thousands, therefore P must be 2. But also, any multiple of 5 must end with 5, so P must be 5. A contradiction !