If a

Question

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

(1) a < c
(2) b < c

BrentGMATPrepNow · Accepted Answer

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

RELATED VIDEO
 https://www.youtube.com/watch?v=S_fjYmCtvy0

Bunuel · Answer

If a < x < b and c < y < d, is x < y ? (1) a < c --> given: a given: x

Bunuel · Answer

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.

fameatop · Answer

1) Insufficient
2) Sufficient

Answer B

sanjoo · Answer

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

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

dexerash · Answer

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

Bunuel · Answer

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.

Carcass · Answer

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

minhaz3333 · Answer

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

JeffTargetTestPrep · Answer

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.

sauravpaul · Answer

(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.

JeffTargetTestPrep · Answer

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

totaltestprepNick · Answer

B https://www.youtube.com/watch?v=62HuwP9lRBo Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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

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