Cryptograms (Set 1 1 , Problem 2 2 )

Algebra Level pending

A S × A S A R K S \large{\begin{array}{ccccccc} && & & A& S&\\ \times && & & A& S&\\ \hline && & & A& R& K&S\\ \end{array}}

Find the value of A R K S + A S + A S ARKS + AS + AS (or A R K S + 2 × A S ARKS + 2 \times AS or A R K S + 2 ( A S ) ARKS + 2(AS) or A R K S + 2 A S ARKS + 2AS )

A = S + 4 A = S + 4

Note: A , S , R , K A, S, R, K are different.


The answer is 9215.

Yajat Shamji by Yajat Shamji , 16, United Kingdom

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1 solution

Yajat Shamji
Jul 7, 2020

Since S 2 = S S^2 = S , S = 5 S = 5 .

Now since A = S + 4 A = S + 4 , A = 5 + 4 = 9 A = 5 + 4 = 9

Now 9 5 2 = 9 R K 5 95^2 = 9RK5

9 5 2 = 95 × 95 = 9025 95^2 = 95 \times 95 = 9025

R = 0 , K = 2 R = 0, K = 2

Now, since the answer is in the format A R K S + A S + A S ARKS + AS + AS , 9025 + 95 + 95 = 9215 9025 + 95 + 95 = 9215

Answer → 9215 \rightarrow \fbox{9215}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

@Yajat Shamji : Although you're answer is correct, S 2 = S ( mod 10 ) S^{2}=S(\text{mod }10) doesn't imply that S = 5 S=5 . S S could be 0 0 , 1 1 , 5 5 , or 6 6 . You need to check each case to be sure that you have the right answer.

Ved Pradhan - 11 months, 1 week ago

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Because A = S + 4 A = S + 4 , you mean, 0 , 1 , 5 0, 1, 5 .

Yajat Shamji - 11 months, 1 week ago

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