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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