Multiple choice general knowledge math & puzzles

Two positive integers differ by 4 and the sum of their reciprocals is 10/21. One of the numbers is:

  1. 3

  2. 1

  3. 5

  4. 21
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A Correct answer
Explanation

Let the numbers be $x$ and $x+4$. The equation $1/x + 1/(x+4) = 10/21$ simplifies to $10x^2 + 40x = 42x + 84$, or $5x^2 - x - 42 = 0$. Solving gives $x=3$. Thus the numbers are 3 and 7. Option 20964 is correct.

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