Question

The U.S. Senate is composed of 2 senators from each of the 50 states. In order for a treaty to be ratified, at least two thirds of the senators present must approve the treaty. Suppose all senators are present and 48 of them have voted in favor of a treaty. What are the possible numbers of additional senators who must vote in favor of the treaty in order to ratify it?

Answer 1

19 or more

Explanation:

Answer 2

There are 2 senators from each of the 50 states.
All senators are present, therefore there are 100 senators.

48 senators voted in favor of a treaty.
Let x = the number of additional senators who should vote in favor of the treaty to achieve 2/3 of 100.
That is,
48 + x ≥ (2/3)100
x ≥ 200/3 - 48
x ≥ 18.667

x should be an integer, therefore
x ≥ 19

Answer: 19 or greater