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xy^2z^3>0
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28 Dec 2021, 06:31
28 Dec 2021, 06:31
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33% (01:25) wrong based on 27 sessions
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\(xy^2z^3>0\)
\(xyz<0\)
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
\(xyz<0\)
Quantity A |
Quantity B |
y |
xz |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
xy^2z^3>0
[#permalink]
28 Dec 2021, 06:47
28 Dec 2021, 06:47
The answer should be B. In the first inequality, only the true nature of y is not known as it is raised to an even exponent (even exponents put a mask on the negativity of a number or variable, while there is no room for hiding with odd exponents: think Phil Collin's True Colours). So, for x and z that are both raised to odd exponents, it is thus the case that they are either both positive or both negative, for the inequality to be positive. They essentially have the same sign.
The second inequality shows that when y is now raised to an odd exponent like x and z, and its true nature is also known, the result is negative. This unequivocally shows y to be a negative (its true colours that were previously masked are now shining through).
As such, Column A is a negative number. Column B will always be a positive number since x and z have the same sign whether they are positive or negative and their product will always give a positive number. B is thus the correct answer choice.
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The second inequality shows that when y is now raised to an odd exponent like x and z, and its true nature is also known, the result is negative. This unequivocally shows y to be a negative (its true colours that were previously masked are now shining through).
As such, Column A is a negative number. Column B will always be a positive number since x and z have the same sign whether they are positive or negative and their product will always give a positive number. B is thus the correct answer choice.
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Re: xy^2z^3>0
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28 Dec 2021, 09:01
28 Dec 2021, 09:01
1
Carcass wrote:
\(xy^2z^3>0\)
\(xyz<0\)
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
\(xyz<0\)
Quantity A |
Quantity B |
y |
xz |
The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Given: \(xy^2z^3>0\)
Since \(y^2\) must be positive, we can safely divide both sides by \(y^2\) to get: \(xz^3>0\)
Similarly, since \(z^2\) must be positive, we can safely divide both sides by \(z^2\) to get: \(xz>0\)
In other words, \(xz\) is positive.
Given: \(xyz<0\)
Since we just learned that \(xz\) is positive, we can safely divide both sides by \(xz\) to get: \(y < 0\)
In other words, \(y\) is negative.
Answer: B
