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

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:

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If a < x < b and c < y < d, is x < y ?

(1) a < c --> given: a<x, c<y and a<c. Now, if a<(c<y)<x then the answer is NO but if a<x<(c<y) then the answer is YES. Not sufficient.

(2) b < c --> given: x<b, c<y and b<c, so x<(b<c)<y, which means that x<y. Sufficient.

Answer: B.
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SOLUTION

If a < x < b and c < y < d, is x < y ?

(1) a < c. From this statement we cannot determine whether \(x < y\). For example, consider that \(a\) and \(c\) are some negative numbers and \(x\) and \(y\) are some positive numbers, we can have that \(x<y\) as well as \(y<x\). Not sufficient.

(2) b < c. Since, \(b<c\), then \(a < x < b<c < y < d\) --> \(x<y\). Sufficient.

Answer: B.
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1) Insufficient
2) Sufficient

Answer B

Statement 1: A <c... insufficient...


Statement. 2 ...sufficient..because B<c.. X must be less than Y..
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x < y?

(1)
a < x < b
c < y < d
and a < c
these 2 eqns can be combined in multiple ways

a...x...b...c...y...d
or
a...c..y...d...x..b
etc.
Thus, x can be greater or lesser than y
So, this is not sufficient

(2)
a < x < b
c < y < d
and b < c

these 3 eqns can be fit only in one way
a...x...b...c...y...d
=> x < y

Thus this is sufficient.

Hence B

SOLUTION

If a < x < b and c < y < d, is x < y ?

(1) a < c. From this statement we cannot determine whether \(x < y\). For example, consider that \(a\) and \(c\) are some negative numbers and \(x\) and \(y\) are some positive numbers, we can have that \(x<y\) as well as \(y<x\). Not sufficient.

(2) b < c. Since, \(b<c\), then \(a < x < b<c < y < d\) --> \(x<y\). Sufficient.

Answer: B.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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This one is tricky because we could assume right away that we need both stats ar at least 3 elements to have an answer

1) a < c we do not know nothing about B (in this case we can see B as a pivotal element)

2) b < c thi is suff because in the chain a < b AND b < c the c < d........

B is the answer
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from stat 1 -
a < c
assigning a, b, c , d few numbers would give us easy approach
a=2 , b = 4 , c= 3 (a<c) , d = 5
now 2<x<4 and 3<y<5
for x = 3.9 and y = 3.1
Stat 1 insufficient

from this we can say if c would be greater than b then x would be definitely less then y
say b = 4 and c = 5 .
stat 2 is sufficient alone.
correct - B

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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(1) is insufficient obviously.

(2) says b < c. So then, if we combine both inequalities given in the question, we have: a < x < b < c < y < d.
So, we know that x < y. So, sufficient.

Hence B.

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
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