Bunuel wrote:
Solution:
We are given that a < x < b, and that c < y < d. We must determine whether x < y.
Statement One Alone:a < c
From the information in statement one we know that a (the smallest value in the inequality a < x < b) is less than c (the smallest value in the inequality c < y < d). However, that information still does not allow us to determine whether x is less than y.
For example, let a = 1, c = 2, x = 2, and y = 3. In this scenario x is less than y.
However, if a = 1, c = 2, x = 4, and y = 3, then x is greater than y.
Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:b < c
Using the information in statement two we know that b (the largest value in the inequality a < x < b) is less than c (the smallest value in the inequality c < y < d). Thus we know that
x must be less than y. To support this conclusion we can use a few convenient numbers.
Let’s say b = 5 and c = 6. Thus we can say:
a < x < 5 and 6 < y < d
We see that x must be less than 5 and y must be greater than 6. Once again, this tells us that
x must be less than y. Statement two is sufficient to answer the question.
The answer is B.
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