How many two-digit numbers yield a remainder of 1 when divided by both 4 and 14?

A. 0 B. 1 C. 2 D. 3 E. 4

(D) Let’s use n to denote a two-digit number that fits the requirement in the question.

Since we are looking for a remainder of 1 when n is divided by 4 or 14, then (n – 1) must be divisible by both 4 and 14. All numbers divisible by both 4 and 14 must be divisible by their least common multiple, which is 28.

So n – 1 can equal any two-digit multiple of 28. These possible values are: n – 1 = 28, 56, or 84.

Therefore, n = 29, 57, or 85 (3 different two-digit numbers).

The correct answer is choice (D). ----------

43 is also another number that yeild a remainder of 1 when divided by both 4 and 14. So the answer should be D.

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