If a < x < b and c < y < d

jjjinapinch wrote:If a < x < b and c < y < d, is x < y ?
(1) a < c
(2) b < c

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.

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.

Answer: B