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Reciprocals

Expert replies
by yellowho » Sun Mar 06, 2011 1:30 am
If non-zero x is the reciprocal of y, then which of the following may be true?

a)x/(1/y)=1/2
b)(1/x)/y=2
c) (1/y)/x=1/2
d) (1/x)/(1/y)=1/2
e) y/(1/x)=2
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Source: — Problem Solving |

by manpsingh87 » Sun Mar 06, 2011 1:58 am
yellowho wrote:If non-zero x is the reciprocal of y, then which of the following may be true?

a)x/(1/y)=1/2
b)(1/x)/y=2
c) (1/y)/x=1/2
d) (1/x)/(1/y)=1/2
e) y/(1/x)=2

IMO D..!!! as per the given condition we have x=1/y; now by submitting these values we get d as a probable answer..!!!!
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by Night reader » Sun Mar 06, 2011 2:17 am
x<>0, x=1/y
a) x=1/2 * 1/y= 1/2y
b) 1/xy=2, xy=1/2, x=1/2y
c) 1/xy=1/2, xy=2, x=2/y
d) y/x=1/2, 2y=x
e) xy=2, x=2/y

IOM d
yellowho wrote:If non-zero x is the reciprocal of y, then which of the following may be true?

a)x/(1/y)=1/2
b)(1/x)/y=2
c) (1/y)/x=1/2
d) (1/x)/(1/y)=1/2
e) y/(1/x)=2
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by nk_81 » Sun Mar 06, 2011 3:17 am
Hi, Can anyone elaborately explain this answer? I haven't understood the approach as none of the solution turns up true. I tried testing with x=1 and then x=2

Thanks
NK
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by Anurag@Gurome » Sun Mar 06, 2011 3:38 am
yellowho wrote:If non-zero x is the reciprocal of y, then which of the following may be true?

a)x/(1/y)=1/2
b)(1/x)/y=2
c) (1/y)/x=1/2
d) (1/x)/(1/y)=1/2
e) y/(1/x)=2
x = 1/y => y = 1/x

Now, each of the options except option D are wrong as all of them will be equal to 1. Let's check,
  • A) x/(1/y) = x/x = 1
    B) (1/x)/y = y/y = 1
    C) (1/y)/x = x/x = 1
    E) y/(1/x) = y/y = 1
But option D is (1/x)/(1/y) = (1/x)/x = 1/x² = y²

Hence, value of option D depends upon value of x or y.
Therefore, it is possible that option D has the value 1/2 for x = √2, i.e. y = 1/(√2)
But all the other options are not feasible at all.

The correct answer is D.
nk_81 wrote:I tried testing with x=1 and then x=2
The problem says may be true not always true.
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