Official Explanation
Infer
It is given that the ratio of twin births to all births is a constant. Let t1, t2, b1, and b2 represent twin births in two different years and all births in those same two years, respectively, where each of t1, t2, b1, and b2 is positive. If the fraction with numerator t sub 1 and denominator b sub 1 equals the fraction with numerator t sub 2 and denominator b sub 2, then t1 b2 = t2b1. If t2 > t1, then t2b1 > t1b1 and so t1 b2 > t1b1 by substitution. It follows that b2 > b1. Therefore, the year with the greatest number of twin births will have the greatest number of births and the year with the least number of twin births will have the least number of births.
RO1: Infer
Year 4 had the greatest number of twin births and therefore had the greatest number of births.
The correct answer is 4.
RO2: Infer
Year 17 had the least number of twin births and therefore had the least number of births.
The correct answer is 17.
Alternatively, letting K be the constant of proportionality of twin births to all births, it follows that Number of twin births in Year cap N over Number of all births in Year cap N equals K and 1 over K (Number of twin births in Year N) = Number of all births in Year N. Thus, the number of all births for Years 1, 2, 3, …, 17, respectively, are 365 over K, 560 over K, 510 over K, …, 239 over K. Of these, the greatest is 627 over K in Year 4 and the least is 239 over K in Year 17.