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23 Oct 2019, 02:30
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A
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If \(wxyz ≠ 0\), does \(wxyz = 1\)?
(1) \(w = \frac{1}{x}\), \(y = \frac{1}{z}\)
(2) \(wx^2 = \frac{1}{xyz}\)
(1) \(w = \frac{1}{x}\), \(y = \frac{1}{z}\)
(2) \(wx^2 = \frac{1}{xyz}\)
Archit3110
23 Oct 2019, 02:33
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Bunuel
#1
\(w = \frac{1}{x}\), \(y = \frac{1}{z}\)
does \(wxyz = 1\)
sufficeint
#2
\(wx^2 = \frac{1}{xyz}\)[/quote]
does \(wxyz = 1\)
no; we get 1/x
insufficient
IMO A
23 Oct 2019, 07:47
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The product of any set of numbers can be ONE in some specific cases only.
One – if all the numbers involved are equal to 1 or -1. While dealing with -1, be careful about the number of terms since there's a negative sign involved.
Two – if we have numbers and their reciprocals being multiplied together.
The question data says that the product of the numbers w, x, y and z is not equal to 0. This means that none of the values are equal to 0.
From statement I alone, we know that w and x are reciprocals; so are y and z. Therefore, the product of these numbers will be 1.
Statement I alone is sufficient. Answer options B, C and E can be eliminated. Possible answer options are A or D.
From statement II alone, w\(x^2\) = \(\frac{1}{xyz}\). Since we need to check if wxyz = 1, we can swap the terms and rewrite the equation above as, wxyz = \(\frac{1}{x^2}\).
wxyz will be equal to 1 depending on whether x is equal to 1/-1 or not. Therefore, statement II alone is insufficient to answer the question with a unique Yes or No.
Answer option D can be eliminated. The correct answer option is A.
Always focus on what you are trying to find in the question and try to rewrite the expression/equation to obtain what you want on the LHS.
Hope that helps!
One – if all the numbers involved are equal to 1 or -1. While dealing with -1, be careful about the number of terms since there's a negative sign involved.
Two – if we have numbers and their reciprocals being multiplied together.
The question data says that the product of the numbers w, x, y and z is not equal to 0. This means that none of the values are equal to 0.
From statement I alone, we know that w and x are reciprocals; so are y and z. Therefore, the product of these numbers will be 1.
Statement I alone is sufficient. Answer options B, C and E can be eliminated. Possible answer options are A or D.
From statement II alone, w\(x^2\) = \(\frac{1}{xyz}\). Since we need to check if wxyz = 1, we can swap the terms and rewrite the equation above as, wxyz = \(\frac{1}{x^2}\).
wxyz will be equal to 1 depending on whether x is equal to 1/-1 or not. Therefore, statement II alone is insufficient to answer the question with a unique Yes or No.
Answer option D can be eliminated. The correct answer option is A.
Always focus on what you are trying to find in the question and try to rewrite the expression/equation to obtain what you want on the LHS.
Hope that helps!
