Last visit was: 26 Jul 2024, 20:39 It is currently 26 Jul 2024, 20:39
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 94619
Own Kudos [?]: 644177 [13]
Given Kudos: 86770
Send PM
CAT Tests Forum Quiz Mode
If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 [#permalink] If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0   08 Sep 2021, 04:00
13
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

59% (01:35) correct 41% (01:28) wrong based on 261 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
If ab ≠ 0 and ax – by < 0, is x < y ?

(1) a = b
(2) a^3 > 0
ShowHide Answer
Official Answer
C
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30868 [0]
Given Kudos: 799
Location: Canada
Send PM
Re: If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 [#permalink] If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0   08 Sep 2021, 10:22
Expert Reply
Top Contributor
Bunuel wrote:
If ab ≠ 0 and ax – by < 0, is x < y ?

(1) a = b
(2) a^3 > 0


Given: ab ≠ 0 and ax – by < 0

Target question: Is x < y ?

Statement 1: a = b
Since we are given no information about the values of x and y, statement 1 is NOT SUFFICIENT

Statement 2: a^3 > 0
Since we are given no information about the values of x and y, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that a = b
Statement 2 tells us that y is positive
So, the statements combined tell us that a and b are not only equal but both positive.

Let's see what happens if we take the given inequality (ax – by < 0) and substitute b for a.
We get: bx – by < 0
Factor: b(x – y) < 0
Since we know that b is positive, it must be the case that (x - y) is negative.
In other words, x - y < 0
Add y to both sides of the inequalities to get: x < y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
User avatar
G
TestPrepUnlimited
Tutor
Joined: 17 Sep 2014
Posts: 1245
Own Kudos [?]: 975 [0]
Given Kudos: 6
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Send PM
Re: If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 [#permalink] If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0   08 Sep 2021, 21:07
Expert Reply
Bunuel wrote:
If ab ≠ 0 and ax – by < 0, is x < y ?

(1) a = b
(2) a^3 > 0


Statement 1:

We may rewrite the inequality as a*(x - y) < 0. Insufficient.

If we knew \(a\) was positive, then \(x - y\) would be negative.

Statement 2:

We can cube root both sides to get \(a > 0\). Insufficient.

Combined:

Now we know x - y must be negative. Hence x - y < 0 and x < y. sufficient.

Ans: C
User avatar
G
Mck2023
Manager
Manager
Joined: 23 Feb 2020
Posts: 133
Own Kudos [?]: 87 [1]
Given Kudos: 297
Location: Nepal
GMAT 1: 650 Q44 V35
Send PM
Re: If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 [#permalink] If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0   14 Sep 2021, 21:42
TestPrepUnlimited wrote:
Bunuel wrote:
If ab ≠ 0 and ax – by < 0, is x < y ?

(1) a = b
(2) a^3 > 0


Statement 1:

We may rewrite the inequality as a*(x - y) < 0. Insufficient.

If we knew \(a\) was positive, then \(x - y\) would be negative.

Statement 2:

We can cube root both sides to get \(a > 0\). Insufficient.

Combined:

Now we know x - y must be negative. Hence x - y < 0 and x < y. sufficient.

Ans: C


Can we cube root an inequality? Please shed some lights.
User avatar
L
CrackverbalGMAT
GMAT Club Legend
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4915
Own Kudos [?]: 7820 [0]
Given Kudos: 221
Location: India
Send PM
Re: If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 [#permalink] If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0   26 Oct 2021, 05:15
Top Contributor
Statement 1: \(a=b\)
\(ax-ay <0\)
\(a(x-y) <0\)

For the Product of 2 terms to be negative, one of the term should be positive and other one should be negative. Hence there are 2 possible cases here


Case 1 : \(a<0 \) and \(x-y >0\) i.e \(x > y \)

is x < y? No
​
Case 2: \(a>0 \)and \(x-y <0 \) i.e x<y
is x < y? Yes
​
Since you are getting both YES and NO for the same question stem, Statement 1 alone is not sufficient.

Statement 2: \(a^3 > 0\)
Statement 2 alone is clearly insufficient as we don't have any idea about b.

Combing both statements, we can conclude that \(a>0\) i.e Case 2 in St.1 as its given that \(a^3 >0\) in St.2

Case 2: a>0 and x-y <0 i.e x<y
is x < y? Yes
Hence, we are able to get a definite answer to the question stem is x < y?.
Option C is the answer.

Thanks,
Clifin J Francis,
GMAT SME
User avatar
S
woohoo921
Director
Director
Joined: 04 Jun 2020
Posts: 542
Own Kudos [?]: 74 [0]
Given Kudos: 623
Send PM
If ab 0 and ax by < 0, is x < y ? (1) a = b (2) a^3 > 0 [#permalink] If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0   09 Jul 2022, 11:24
CrackverbalGMAT wrote:
Statement 1: \(a=b\)
\(ax-ay <0\)
\(a(x-y) <0\)

For the Product of 2 terms to be negative, one of the term should be positive and other one should be negative. Hence there are 2 possible cases here


Case 1 : \(a<0 \) and \(x-y >0\) i.e \(x > y \)

is x < y? No
​
Case 2: \(a>0 \)and \(x-y <0 \) i.e x<y
is x < y? Yes
​
Since you are getting both YES and NO for the same question stem, Statement 1 alone is not sufficient.

Statement 2: \(a^3 > 0\)
Statement 2 alone is clearly insufficient as we don't have any idea about b.

Combing both statements, we can conclude that \(a>0\) i.e Case 2 in St.1 as its given that \(a^3 >0\) in St.2

Case 2: a>0 and x-y <0 i.e x<y
is x < y? Yes

Hence, we are able to get a definite answer to the question stem is x < y?.
Option C is the answer.

Thanks,
Clifin J Francis,
GMAT SME


CrackverbalGMAT
Thank you for this helpful explanation.

I am hoping to clarify if I tested cases correctly to disprove that statement 1 was insufficient.
Case 1:
Let a=2 so b=2 because a=b
2X - 2Y < 0 -->
2X < 2Y -->
X < Y

Case 2: Let a=-2 so b=-3 because a=b
-3X - - 3Y < 0 -->
-3x + 3Y < 0 -->
-3x < -3Y
Flip the signs because both are negative
X > Y
I am not sure if my math is correct for Case 2 above.

Thank you for your time and help.

ScottTargetTestPrep
avatar
B
suhailblotra
Intern
Intern
Joined: 22 Oct 2021
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 1
Send PM
Re: If ab 0 and ax by < 0, is x < y ? (1) a = b (2) a^3 > 0 [#permalink] If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0   14 Jul 2022, 21:26
1
Kudos
why cant ax<by from the question stem
s1.
a=b,which implies x<y s1 sufficient
avatar
B
Dhruva2000
Intern
Intern
Joined: 19 Jan 2022
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 58
Send PM
Re: If ab 0 and ax by < 0, is x < y ? (1) a = b (2) a^3 > 0 [#permalink] If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0   15 Jul 2022, 01:54
TestPrepUnlimited wrote:
Bunuel wrote:
If ab ≠ 0 and ax – by < 0, is x < y ?

(1) a = b
(2) a^3 > 0


why shouldn't we move the second variable in (ax – by < 0) to the right of the sign and convert the eq to this ax<by?

By doing that we can get a sufficient answer using st. 1, that's where I went wrong. need some guidance on whats the thought process on few question where we do that i.e. move the variable to the other side..!
GMAT Club Bot
gmatclubot
Re: If ab 0 and ax by < 0, is x < y ? (1) a = b (2) a^3 > 0 [#permalink]
15 Jul 2022, 01:54
Moderator:
Bunuel
Math Expert
94619 posts