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Difficulty:
25%
(medium)
Question Stats:
77% (01:33) correct
23%
(01:48)
wrong
based on 180
sessions
History
Date
Time
Result
Not Attempted Yet
Let \(\frac{x}{y} + \frac{w}{z} = 2\). Then the value of \(\frac{y}{x} + \frac{z}{w}\) is
(A) 1/2
(B) 3/4
(C) 1
(D) 5
(E) It cannot be determined from the information given.
_________________
(A) 1/2
(B) 3/4
(C) 1
(D) 5
(E) It cannot be determined from the information given.
_________________
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Posts: 6,727
Bunuel
A fast approach is to identify values for w, x, y and z that satisfy the given equation, \(\frac{x}{y} + \frac{w}{z} = 2\)
One set of values is w = 1, x = 1, y = 1 and z = 1
Now plug these values into the target expression.
We get: \(\frac{y}{x} + \frac{z}{w} = \frac{1}{1} + \frac{1}{1}\)
\(= 1 + 1\)
\(= 2\)
Since 2 is not among the first four answer choices, the correct answer must be ....
Xin Cho
\(\frac{x}{y}\) + \(\frac{w}{z}\) = 2
or \(\frac{xz +yw}{yz}\) = 2
or \({xz +yw}\) = 2yz
Now, \(\frac{y}{x}\) + \(\frac{z}{w}\)=\(\frac{yw+xz}{xw}\) = \(\frac{2yz}{xw}\)..... Thus cannot be determined with given info......Option E
Let \(\frac{x}{y} = a\) and \(\frac{w}{z} = b\)
=> a + b = 2
We need to find the value of \(\frac{1}{a} + \frac{1}{b}\) = \(\frac{a+b}{ab}\)
We know the value of a + b but we don't know the value of a*b
Hence option E
_________________
=> a + b = 2
We need to find the value of \(\frac{1}{a} + \frac{1}{b}\) = \(\frac{a+b}{ab}\)
We know the value of a + b but we don't know the value of a*b
Hence option E
_________________
Is the answer not A.1/2 because \(\frac{x}{y}\) + \(\frac{w}{z}\) is not reciprocal of \(\frac{y}{x}\) + \(\frac{z}{w}\)?
Xin Cho
\(\frac{x}{y}\) + \(\frac{w}{z}\) is NOT reciprocal of \(\frac{y}{x}\) + \(\frac{z}{w}\)
\(\frac{x}{y}\) + \(\frac{w}{z}\) = \(\frac{xz+wy}{yz}\) ------- 1
\(\frac{y}{x}\) + \(\frac{z}{w}\) = \(\frac{wy+xz}{xw}\) -------- 2
1 and 2 are not reciprocal to each other.
_________________
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