Discussion
The sum of two positive integers is 200, and their ratio is 7 : 3. What is their greatest common divisor ?
Answer: B
The greatest common divisor is 20.
Split 200 in the ratio 7 : 3. The ratio has 10 parts, so each part is 20:
\[ \begin{aligned} 7 \times 20 &= 140 \\ 3 \times 20 &= 60 \end{aligned} \]
Since 7 and 3 have no common factor, the greatest common divisor of 140 and 60 is the size of one part, 20. Check: 140 = 20 × 7 and 60 = 20 × 3, and 7 and 3 share no further factor.
10 divides both numbers but is not the greatest common divisor. 30 and 40 do not divide both: 30 does not divide 140, and 40 does not divide 60.
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