Question

RATS×4 is equals to STAR each instance of a letter stands for the same digit No two letters represent the same digit and R cannot be zero what is the value of a + s

Answer 1

⭐ Number theory ⭐

RATS × 4 = STAR 

⇒ $R \equiv 4S \ (mod\ 10)$

⇒ $; 4R \leq 9 \ ; 4R + \bigl [ 4A\ (mod 10) \bigr ] = S$

∴ $R = 2 \ and \ S = 8$

Now, 

⇒ $2AT8 \times 4 = 8TA2$

⇒ $\overline{(4A)(4T + 3)} = \overline{TA}$

⇒ $(40A) + (4T + 3) = 10T + A$

⇒ $39 A + 3 = 6T$

⇒ $13A + 1 = 2 T$

In this Last equation , we know that A and T ∈ [1,9] and they are integral. 

The only solution satisfying this will be when A = 1 and T = 7.