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Bunuel
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If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 08 Sep 2021, 04:00
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C
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Difficulty:

45% (medium)

Question Stats:

59% (01:36) correct 41% (01:28) wrong based on 263 sessions

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If ab ≠ 0 and ax – by < 0, is x < y ?

(1) a = b
(2) a^3 > 0
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C
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BrentGMATPrepNow
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If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 08 Sep 2021, 10:22
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Bunuel
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

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Brent
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If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 08 Sep 2021, 21:07
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Bunuel
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
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If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 14 Sep 2021, 21:42
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Bunuel
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.
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If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 26 Oct 2021, 05:15
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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
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If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 09 Jul 2022, 11:24
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CrackverbalGMAT
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
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If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 14 Jul 2022, 21:26
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why cant ax<by from the question stem
s1.
a=b,which implies x<y s1 sufficient
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Dhruva2000
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If ab ≠ 0 and ax – by < 0, is x < y ? (1) a = b (2) a^3 > 0 15 Jul 2022, 01:54
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Bunuel
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..!
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Bunuel
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