|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
01 Dec 2021, 06:00
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
56% (02:39) correct
44%
(02:40)
wrong
based on 135
sessions
History
Date
Time
Result
Not Attempted Yet
If \(y > 0\), is \(\frac{x}{y} < 3\)?
(1) \(x(x + y) − 4y(x + y) < 0\)
(2) \(5(y + 8) < 20y – 3x + 40\)
(1) \(x(x + y) − 4y(x + y) < 0\)
(2) \(5(y + 8) < 20y – 3x + 40\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
01 Dec 2021, 09:53
Kudos
Bookmarks
Since y > 0 we can first rephrase the question stem:
Is X < 3Y?
(1) factoring the (x + y) common factor:
(X + Y) (X - 4Y) < 0
Since the product is less than 0, the factors must have opposite signs. So we have two possible cases:
Case 1:
(X + Y) < 0
And
(X - 4Y) > 0
Which means:
X < -Y
And
X > 4Y
Since Y is a positive value, it means that if Y were +1, for instance, these inequalities would be impossible to coexist
X <-1 ——-and——— X > 4
X can not simultaneously be less than a (-)negative number and greater than a (+)positive number. So it must be the other case
Case 2:
(X + Y) > 0
and
(X - 4Y) < 0
X > -Y —- and —— X < 4Y
Combining the inequalities:
-Y < X < 4Y
*Q* is: X < 3Y?
Not sure:
Can have
-Y < 3Y < X < 4Y ——> NO
OR
-Y < X < 3Y < 4Y ——> YES
S1 not sufficient
(2)
5Y + 40 < 20Y - 3X + 40
3X < 15Y
X < 5Y
*Q* is X < 3Y?
Not sure —- S2 is not sufficient alone
Together: statement 2 does not add any more of a restrictive condition on X
All we know for sure is that: X < 4Y
We do not know whether: X < 3Y
Answer
E
Posted from my mobile device
Is X < 3Y?
(1) factoring the (x + y) common factor:
(X + Y) (X - 4Y) < 0
Since the product is less than 0, the factors must have opposite signs. So we have two possible cases:
Case 1:
(X + Y) < 0
And
(X - 4Y) > 0
Which means:
X < -Y
And
X > 4Y
Since Y is a positive value, it means that if Y were +1, for instance, these inequalities would be impossible to coexist
X <-1 ——-and——— X > 4
X can not simultaneously be less than a (-)negative number and greater than a (+)positive number. So it must be the other case
Case 2:
(X + Y) > 0
and
(X - 4Y) < 0
X > -Y —- and —— X < 4Y
Combining the inequalities:
-Y < X < 4Y
*Q* is: X < 3Y?
Not sure:
Can have
-Y < 3Y < X < 4Y ——> NO
OR
-Y < X < 3Y < 4Y ——> YES
S1 not sufficient
(2)
5Y + 40 < 20Y - 3X + 40
3X < 15Y
X < 5Y
*Q* is X < 3Y?
Not sure —- S2 is not sufficient alone
Together: statement 2 does not add any more of a restrictive condition on X
All we know for sure is that: X < 4Y
We do not know whether: X < 3Y
Answer
E
Posted from my mobile device
13 Nov 2025, 07:47
Kudos
Bookmarks
Bunuel
To verify whether \(\frac{x}{y} < 3\)
=> \(x < 3y\) since y > 0
(1) \(x(x + y) − 4y(x + y) < 0\)
=> \((x - 4y)(x + y) < 0\)
Given y > 0, let's take the below cases
Note - x = 0 case is already true since it gives a negative number
Case 1) x > 0
\((x + y) > 0\) hence \((x - 4y) < 0\)
=> \(x - 4y < 0\)
=> \(x < 4y\)
Case 2) x < 0
=> \((x - 4y) < 0\) hence \((x + y) < 0\)
=> \((x + y) < 0\)
=> \(x < -y\)
Range of x becomes
=> \(-y < x < 4y\)
This includes x = 0 as well
Insufficient
(2) \(5(y + 8) < 20y – 3x + 40\)
=> \(5y + 40 < 20y – 3x + 40\)
=> \(-15y < -3x\)
=> \(15y > 3x\)
=> \(5y > x\)
Insufficient
Combining we get
\(-y < x < 4y\) and \(x < 5y\)
Still insufficient
Option E
