If ab ≠ 0 and ax – by

Question

If ab ≠ 0 and ax – by < 0, is x < y ?

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

BrentGMATPrepNow · Answer

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

TestPrepUnlimited · Answer

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

Mck2023 · Answer

Can we cube root an inequality? Please shed some lights.

CrackverbalGMAT · Answer

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 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

woohoo921 · Answer

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

suhailblotra · Answer

why cant ax<by from the question stem
s1.
a=b,which implies x<y s1 sufficient

Dhruva2000 · Answer

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..!

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards