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Exponents question..need simple solution

Expert replies
Source: — Data Sufficiency |

by melguy » Tue Aug 06, 2013 5:27 am
Info from the question
vmt ≠ 0 i.e. v, m or t are not 0.

Question is asking is (v^2)(m^3)(t^-4) > 0 i.e. is m positive (note v or t can be positive or negative but end result will always be positive considering even a negative value raised to the power of a positive value yields a positive result i.e. -2 ^ 2 = + 4)

Statement 1
m > v^2
Result v^2 will always be a positive value.
i.e. m is positive so the whole equation is positive.

The statement is sufficient.

Statement 2
m > t^-4
m > 1 / t^4
Result of 1 / t^4 will always be a positive value.
i.e. m is positive so the whole equation is positive.

The statement is sufficient.

In my opinion the Answer is D
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by [email protected] » Tue Aug 06, 2013 11:31 am
Hi melguy,

Very nice analysis and step-by-step explanation. You'll find a few opportunities on Test Day to use the EXACT same logic/approach on some Quant questions. Look in DS (and the occasional PS question) for these opportunities. These questions usually involve number properties (pos/neg, odd/even) and can be solved quickly if you know your number properties and can spot them when they appear.

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by Matt@VeritasPrep » Tue Aug 06, 2013 12:33 pm
The earlier explanation is dead on. Just to supply the algebra, I'll add a little bit.

Before going to the two statements, try to extract as much as you can from the question stem. We know:

v² ≥ 0 for any value of v (on the GMAT)
t-� = 1/t� = (1/t²)², and as above, anything squared ≥ 0, so (1/t²)² ≥ 0 for any value of t

Since the stem tells us v*m*t ≠ 0, we know v ≠ 0 and t ≠ 0, so v² > 0 and (1/t²)² > 0.

That means the only think we need to know is whether m is positive or negative: the result of a base raised to an odd power has the same sign as its base. (In other words, if m < 0, m³ < 0, and if m > 0, m³ > 0.) This means we can rephrase the question as "Is m positive?"

S1:: m > v², and v² > 0, so m > 0, SUFFICIENT.
S2:: m > 1/t� and 1/t� > 0, so m > 0, SUFFICIENT.
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