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

Question

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

(1)  m > v^2

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

Bunuel · Accepted Answer

If  v*m*t  not  = 0 , is  v^2*m^3*t^{-4} > 0 ?

v*m*t
eq{0}  means that none of the unknowns equals to zero.

Is  v^2*m^3*t^{-4}>0 ?

Is  \frac{v^2*m^3}{t^4}> 0 ?

Since  v^2  and  t^4  are positive (recall that none of the unknowns equals to zero) this inequality will hold true if and only  m^3>0 , or, which is the same, when  m>0 .

(1)  m>v^2  -->  m  is more than some positive number ( v^2 ), hence  m  is positive. Sufficient.

(2)  m>t^{-4}  -->  m>\frac{1}{t^4}  --> again  m  is more than some positive number ( \frac{1}{t^4}  ), hence  m  is positive. Sufficient.

Answer: D.

Hope it's clear.

ritula · Answer

It shld be D
Is  v^2 *m^3*t^-4>0? 
Since  v^2  and  1/t^4 are positive, so it depends upon whether m is positive or not
(1) m> v^2  >0 hence sufficient
(2) m>  1/t^4  >0 hence sufficient

swatirpr · Answer

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

amanvermagmat · Answer

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

MathRevolution · 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.

bumpbot · Answer

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

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