Multiple choice

x and y are two distinct 2-digit numbers. If their HCF is 14, what is the maximum possible value of x + y?

  1. 42

  2. 196

  3. 28

  4. 182

  5. 154
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D Correct answer
Explanation

x = 14a, y = 14b. For 2-digit numbers, a, b can be 1 to 7. Maximize 14(a+b). Max a, b are 7 and 6 (distinct). 14(7+6) = 14 * 13 = 182.

AI explanation

Since the HCF is 14, both numbers must be multiples of 14. We write the two-digit multiples of 14 as 14, 28, 42, 56, 70, 84, and 98. To maximize the sum, we pick the two largest distinct multiples, which are 98 and 84. Their sum is 98 plus 84, which equals 182.

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