Question

Find the values of letters A and B.

(3 marks)

Answer 1

The first condition is A × 3 gives A as ones digit,
So, A can take values of 0 and 5.
(0.5 marks)

Proceed with any one value and check whether it is satisfying the other conditions or not.
(0.5 marks)

Suppose A = 5, then A × 3 = 5 × 3 = 15, which gives 5(A) as ones digit with 1 as carry.
(0.5 marks)

The second condition is 3B + BA + carry(if any) gives 7 as ones digit. So, 3B + B5 + 1 (carry) gives 7 as ones digit.
(0. 5 marks)

Put values for B which satisfies the above condition,
Suppose B = 2, then 3 × 2 + 2 × 5 + 1(carry) = 17, gives 7 as ones digit with one carry.
(0.5 marks)

The last condition is B × B + carry(if any) gives 5, so 2 × 2 + 1(carry) = 5.
(0.5 marks)

Thus, all the conditions are satisfied with 5 = A and 2 = B.