Is uv 0? (1) u^2v^3

Question

Is  uv > 0 ?

(1)  u^2v^3 < 0

(2)  uv^2 < 0

logro · Answer

We need to find if uv> 0 Statement 1: u^2v^3<0 Irrespective of the sign of u, u^2 will always be positive For the inequality to hold v^3 < 0 which implies that v<0 If u>0, then uv<0 (since v<0) If u<0, then uv>0 Hence Statement 1 alone is insufficient Statement 2: uv^2<0 Since v^2 is always positive, we have u<0 If v < 0, then uv>0 If v>0, then uv<0 Combining Statement 1 and 2 Through statement 1 we know that v<0 and through statement 2 we know that u<0 Hence uv>0 Therefore IMO it is C

BrentGMATPrepNow · Answer

Target question : Is uv > 0? Statement 1 : u²v³ < 0 Since u²v² must be POSITIVE, we can divide both sides of the inequality by u²v² to get: v < 0 We now know that v is NEGATIVE , but we don't know anything about u. So there's no way to answer the target question with certainty Statement 1 is NOT SUFFICIENT Statement 2 : uv² < 0 Since v² must be POSITIVE, we can divide both sides of the inequality by v² to get: u < 0 We now know that u is NEGATIVE , but we don't know anything about v. So there's no way to answer the target question with certainty Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that v is NEGATIVE Statement 2 tells us that u is NEGATIVE So, the product uv = (NEGATIVE)(NEGATIVE) = POSITIVE In other words, uv > 0 Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C Cheers, Brent

nehasomani33 · Answer

Is uv>0?

(1) u2v3<0
(2) uv2<0

Modify the question asked - are u and v in the same sign?

(1) u^2 will always be positive.. so if the product of u^2 and v^3 is negative --> v is negative - we know nothing about u - Insufficient
(2) Same as (1) - v^2 will always be positive.. so if the product of u and v^2 is negative --> u is negative - we know nothing about v - Insufficient

Combined - (1) & (2) u & v are in the same sign - Sufficient

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 2 variables: Let the original condition in a DS question contain 2 variables. Now, 2 variables would generally require 2 more equations for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 2 more equations to match the numbers of variables and equations in the original condition, the logical answer is C.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find whether uv > 0 ?.

Second and the third step of Variable Approach: From the original condition, we have 2 variables (u, and v).To match the number of variables with the number of equations, we need 2 more equations. Since conditions (1) and (2) will provide 2 equations, C would most likely be the answer.

Let’s take look at both condition together.

Condition(1) tells us that \(u^2v^3\) < 0.

Condition(2) tells us that \(uv^2\) < 0.

=> Since, \(u^2\) will always be positive, for the product \(u^2v^3\) < 0, 'v' has to be v < 0.

=> Since, \(v^2\) will always be positive, for the product \(uv^2\) < 0, 'u' has to be u < 0.

=> negative * negative = positive: uv > 0 - is uv > 0 - YES

Since the answer is unique YES , both conditions combined together are sufficient by CMT 1.

Both conditions combined together are sufficient.

So, C is the correct answer.

Answer: C

SAVE TIME: By Variable Approach, when you know that we need two equations, we will directly combine the conditions to solve. We will save time in checking the conditions individually.

Is uv > 0? (1) u^2v^3 < 0 (2) uv^2 < 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

GMAT Data Sufficiency (DS) Questions