Question 31 of 31advanced🔧 ApplyShort Answer4 marks

Solve the cryptarithms —

(i)

EF × E = GGG

Answer

E = 3, F = 7, G = 1. Solution: 37×337 \times 3 = 111. Since GGG = 111G and 111 = 3×373 \times 37, we need EF × E = 111 × G. For G = 1: EF × E = 111 = 3×373 \times 37. So E = 3 and EF = 37, giving F = 7.

(ii)

WOW × 5 = MEOW

Answer

W = 5, O = 2, M = 2, E = 6. Solution: 525×5525 \times 5 = 2625. Since WOW × 5 is a 4-digit number, WOW must be between 200 and 1999/5 ≈\approx 399. The last digit of MEOW is W, and W × 5 ends in W, so W = 0 or 5. W cannot be 0 (would make WOW start with 0), so W = 5. Then 5O5×55 \times 5 = ME05. Checking values: 525×5525 \times 5 = 2625, giving M = 2, E = 6, O = 2, W = 5.

Explanation

(i) The chapter shows that GGG represents a 3-digit number with all digits same: 111, 222, ..., 999. Each equals 111 × G. Since 111 = 3×373 \times 37, and we need EF × E = 111 (for G = 1), we get E = 3, EF = 37, so F = 7. (ii) The chapter demonstrates solving cryptarithms by analyzing constraints. W must be 5 (since W × 5 ends in W and W ≠\neq 0). The product 5O5×55 \times 5 must end in 05, and checking values leads to O = 2.

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