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# If non-zero x is the reciprocal of y, then which of the

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Senior Manager
Joined: 21 Oct 2013
Posts: 408
If non-zero x is the reciprocal of y, then which of the  [#permalink]

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02 Mar 2014, 11:22
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Difficulty:

55% (hard)

Question Stats:

65% (02:13) correct 35% (02:10) wrong based on 174 sessions

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If non-zero x is the reciprocal of y, then which of the following may be true?

A. x / (1/y) = 0.5
B. (1/x) / y = 2
C. (1/y) / x = 0.5
D. (1/x)/(1/y) = 0.5
E. y/(1/x) = 2

Hi, can anyone explain this, please.
NOTE: Reciprocal of x = 1/x
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Joined: 16 Oct 2010
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Location: Pune, India
Re: If non-zero x is the reciprocal of y, then which of the  [#permalink]

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02 Mar 2014, 21:54
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goodyear2013 wrote:
If non-zero x is the reciprocal of y, then which of the following may be true?
x / (1/y) = 0.5
(1/x) / y = 2
(1/y) / x = 0.5
(1/x)/(1/y) = 0.5
y / (1/x) = 2

Hi, can anyone explain this, please.
NOTE: Reciprocal of x = 1/x

Given: x = 1/y
then xy = 1
Also, 1/xy = 1

Now look at the options:
(A) x / (1/y) = 0.5 => xy = 0.5 (Not possible. We know xy = 1)

(B) (1/x) / y = 2 => 1/(xy) = 2 (Not possible. We know 1/xy = 1)

(C) (1/y) / x = 0.5 => 1/yx = 0.5 (Not possible. We know 1/xy = 1)

(D) (1/x)/(1/y) = 0.5

(E) y / (1/x) = 2 => yx = 2 (Not possible. We know xy = 1)

Only option (D) is possible.
(1/x)/(1/y) = 0.5
y/x = 1/2
When $$x = \sqrt{2}, y = 1/\sqrt{2}$$, xy = 1, 1/xy = 1 and y/x = 1/2. So option (D) is possible.
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Re: If non-zero x is the reciprocal of y, then which of the  [#permalink]

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02 Mar 2014, 23:18
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goodyear2013 wrote:
If non-zero x is the reciprocal of y, then which of the following may be true?

A. x / (1/y) = 0.5
B. (1/x) / y = 2
C. (1/y) / x = 0.5
D. (1/x)/(1/y) = 0.5
E. y/(1/x) = 2

Hi, can anyone explain this, please.
NOTE: Reciprocal of x = 1/x

Notice that the question asks which of the following COULD be true, not MUST be true.

x is the reciprocal of y means that x=1/y (y=1/x). Now, replace 1/x by y or 1/y by x in the options:

A. x/(1/y) = 0.5 --> x/x = 0.5 --> 1 = 0.5. WRONG.

B. (1/x)/y = 2 --> y/y = 2 --> 1 = 2. WRONG.

C. (1/y)/x = 0.5 --> x/x = 0.5 --> 1 = 0.5. WRONG.

D. (1/x)/(1/y) = 0.5 --> (1/x)/x = 1/2 --> 1/x^2 = 1/2 --> x^2 = 2. Well, this is possible, if $$x=\sqrt{2}$$ or $$x=-\sqrt{2}$$.

E. y/(1/x) = 2 --> y/y = 2 --> 1 = 2. WRONG.

Hope it's clear.
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Re: If non-zero x is the reciprocal of y, then which of the  [#permalink]

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05 Mar 2014, 21:34
In all the options, replace $$\frac{1}{x} = y$$ OR $$\frac{1}{y} = x$$ (as applicable) so that fraction is removed:

A: 1 = 0.5 (Wrong)

B: 1 = 2 (Wrong)

C: 1 = 0.5 (Wrong)

E: 1 = 2 (WRONG)

D:

$$\frac{1}{x^2} = 0.5$$

$$x^2 = 2$$

$$x = \sqrt{2} ; y = \frac{1}{\sqrt{2}}$$

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Re: If non-zero x is the reciprocal of y, then which of the  [#permalink]

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24 Jul 2019, 21:08
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Re: If non-zero x is the reciprocal of y, then which of the   [#permalink] 24 Jul 2019, 21:08
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