If p1 and p2 are the populations and r1 and r2 are the
numbers of representatives of District 1 and District 2,
respectively, the ratio of the population to the number
of representatives is greater for which of the two
districts?
(1) p1 > p2
(2) r2 > r1
Question: Is p1/r1 > p2/r2?
To compare fractions, we multiply the denominator in each fraction by the numerator in the other.
The numerator used in the larger product belongs to the larger fraction.
For example: Is 2/3 > 1/2?
Denominator 2 * numerator 1 = 2*2 = 4.
Denominator 1 * numerator 2 = 3*1 = 3.
Since numerator 1 is used in the larger product, 2/3 > 1/2.
Thus, the DS above can be rephrased:
Is r2*p1 > r1*p2?
Statement 1: p1 > p2.
No information about r1 and r2.
Insufficient.
Statement 2: r2 > r1.
No information about p1 and p2.
Insufficient.
Statements 1 and 2 combined:
Since in the two inequalities r2 and p1 are the larger values, we know that r2*p1>r1*p2.
Sufficient.
The correct answer is
C.
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