If vmt ≠ 0, is (v^2)*(m^3)*(t^(-4)) > 0?

\(V^2\) will always be positive so \(V^2>0\)
Same for \(T^{-4}\) so \(T^{-4} >0\)

Question stem asks whether m is positive or negative (m>0 or m<0)

Yes/No question

1. \(m>v^2\)

Given \(V^2>0\) so m is positive or \(m >0\)
Ans Yes STATEMENT SUFFICIENT

2. \(m>t^{-4}\)

given \(T^{-4}\)so \(T^{-4} >0\)
so m is positive or \(m >0\)
Ans Yes STATEMENT SUFFICIENT

Answer D

WE are given that none of v or m or t is 0. So v^2 and t^4 will definitely be greater than 0 (even powers). All we need to know is whether m^3 > 0 or < 0 (or we need to know whether m is positive or negative).

(1) m > v^2.
Since v^2 is going to be positive, m > v^2.. this means m > 0. Sufficient.

(2) m > 1/t^4
Again t^4 or 1/t^4 are both going to be positive. So this also means m > 0. Sufficient.

Hence D answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 1 variable: Let the original condition in a DS question contain 1 variable. Now, 1 variable would generally require 1 equation 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 1 equation to match the numbers of variables and equations in the original condition, the logical answer is D.

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 \(v^2 * m^3 * t^(-4)\) > 0 ? where vmt ≠ 0.

=> \( \frac{(v^2 * m^3) }{ t^(4)}\) > 0

=> \(v^2\) and \(t^4 \)will always be positive and hence this inequality will hold TRUE if \(m^3\) > 0. That means m > 0.

We have to check is m > 0?

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

Let’s take look at each condition separately.

Condition(1) tells us that \(m > v^2\) .

=> 'm' is greater than a positive number (\(v^2\)) and hence m > 0 - YES

Since the answer is a unique YES , condition(1) alone is sufficient by CMT 1.

Condition(2) tells us that \(m > t^(-4)\) .

=> 'm' is greater than a positive number (\(\frac{1 }{ t^4}\)) and hence m > 0 - YES

Since the answer is a unique YES , condition(2) alone is sufficient by CMT 1.

Each condition alone is sufficient.

So, D is the correct answer.

Answer: D


SAVE TIME: By Variable Approach, when you know that we need 1 equation, we will directly check each condition to be sufficient. We will save time in checking the conditions individually.

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