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LoyalWater
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If vmt ≠ 0, is (v^2)*(m^3)*(t^(-4)) > 0? Updated on: 17 Nov 2017, 03:21
Originally posted by LoyalWater on 02 Feb 2009, 23:05.
Last edited by Bunuel on 17 Nov 2017, 03:21, edited 4 times in total.
Renamed the topic and edited the question.
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D
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72% (01:16) correct 28% (01:44) wrong based on 633 sessions

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


(1) \(m > v^2\)

(2) \(m > t^{(-4)}\)
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D
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Bunuel
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If vmt ≠ 0, is (v^2)*(m^3)*(t^(-4)) > 0? 02 Oct 2012, 01:54
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If \(v*m*t\) not \(= 0\), is \(v^2*m^3*t^{-4} > 0\)?

\(v*m*t\neq{0}\) 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.
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If vmt ≠ 0, is (v^2)*(m^3)*(t^(-4)) > 0? 04 Feb 2009, 04:28
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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
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If vmt ≠ 0, is (v^2)*(m^3)*(t^(-4)) > 0? 22 Jan 2010, 09:31
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If \(v*m*t\) not \(= 0\), is \(v^2*m^3*t^{-4} > 0\)?

1) \(m>v^2\)
2) \(m>t^{-4}\)
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\(V^2\) 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
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If vmt ≠ 0, is (v^2)*(m^3)*(t^(-4)) > 0? 02 Dec 2017, 01:20
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If \(vmt ≠ 0\), is \(v^2*m^3*t^{(-4)} > 0\)?


(1) \(m > v^2\)

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

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
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If vmt ≠ 0, is (v^2)*(m^3)*(t^(-4)) > 0? 16 Oct 2020, 08:09
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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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If vmt ≠ 0, is (v^2)*(m^3)*(t^(-4)) > 0? 31 Mar 2025, 23:11
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