WAEC 2016 Mathematics · Question 22

If 20(mod 9) is equivalent to y(mod 6), find y.

Options

Answer: B. 2

Explanation written with AI and checked against the answer key

Analyze the question This is a modular arithmetic problem. "20 (mod 9)" means the remainder when 20 is divided by 9. We then find y so that the same number is written as y (mod 6). Concept a (mod n) means the remainder when a is divided by n. Solution Step 1: Find 20 (mod 9). 20 = 2 × 9 + 2, so 20 ≡ 2 (mod 9). Step 2: Set this equal to y (mod 6). y (mod 6) = 2 means y leaves a remainder of 2 when divided by 6. Among the options, 2 is the only value that works (1, 3 and 4 give different remainders mod 6, so none equal 2). So y = 2. A note on the other reading Another way to read it is "20 ≡ y (mod 6)" directly, which gives 20 = 3 × 6 + 2, so y = 2. Both readings agree, which is reassuring. Answer: B (2) Exam tip For "a (mod n)" questions, divide a by n and take the remainder. Then check each option by dividing it by the new modulus. If both readings give the same answer, you can be confident.

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