Data Sufficiency

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

Official Guide question
Answer: B

Target question: Is x < y?

Given: a < x < b and c < y < d

Statement 1: a < c
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several scenarios that satisfy statement 1 (AND the given information). Here are two:
Case a: a = 1, x = 2, b = 3, c = 4, y = 5 and d = 6. In this case, x < y
Case b: a = 1, x = 10, b = 11, c = 4, y = 5 and d = 6. In this case, x > y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b < c
Perfect, this information allows us to COMBINE the two given inequalities.
We get: a < x < b < c < y < d
At this point, it is clear that x < y
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

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