The graph shows, for each year of a 17-year period, t

Question

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The graph shows, for each year of a 17-year period, the number of pairs of twins born in Region Z. In that time, the ratio of the number of twin births to the number of all births was essentially constant.

Select from each drop-down menu the option that creates the statement that is most strongly supported by the information provided.

Of the 17 years appearing in the graph, Year  GRAPH_1_PLACEHOLDER  likely had the greatest number of births in Region Z, and Year  GRAPH_2_PLACEHOLDER  likely had the least number of births in Region Z.

ID: 700250

mayankdgmat · Accepted Answer

IMO it's 4,17

Ratio = C

Pair of twins/Total berths = C

Total Births = Pair/C

So total births is directly proportional to Par of twins. So clearly from chart 4 is max and 17 is min

KarishmaB · Answer

We are given the number of pairs of twins, not the number of births. But we are given that the ratio is constant. This means that if this ratio is 1:10, every year, there was 1 pair of twin births for 9 single births. If some year there were 10 pairs of twin births, the number of single births would have been 90 etc.

So in some year, if there were more twin births, it means more single births too and hence more total births.

Of the 17 years appearing in the graph, Year ___  likely had the greatest number of births in Region Z, and Year ___ likely had the least number of births in Region Z.

Year 4 is shown to have greatest number of twin births and year 17 is shown to have least. Hence the greatest number of births (in all) would be greatest in year 4 too and least in year 17.

ANSWER: 4, 17

playthegame · Answer

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.

MalachiKeti · Answer

Just so we get the translation correct do they mean 
every year = Ratio of twin/Total birth is same
So if it is 2:1 in first year then it is 2:1 in second year too?

cheshire · Answer

yep, ratio is constant.

bumpbot · Answer

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The graph shows, for each year of a 17-year period, t

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