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In the following pairs of numbers, which are reciprocals of each other

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In the following pairs of numbers, which are reciprocals of each other  [#permalink]

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New post Updated on: 07 Jul 2019, 00:03
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A
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Originally posted by Bunuel on 24 Jun 2017, 08:19.
Last edited by SajjadAhmad on 07 Jul 2019, 00:03, edited 1 time in total.
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Re: In the following pairs of numbers, which are reciprocals of each other  [#permalink]

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New post 24 Jun 2017, 08:35
Bunuel wrote:
In the following pairs of numbers, which are reciprocals of each other?

I. 1 and 1
II. 1/11 and −11
III. 5 and \(\frac{\sqrt{5}}{5}\)

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) II and III only

The product of a number and its reciprocal is 1.

I. 1 and 1. Yes. 1*1 = 1. Or remember that the only two numbers that are their own reciprocals are 1 and -1. Keep.

II. 1/11 and -11. No. 1/11 * -11 = -1. Reject.

III. 5 and \(\frac{\sqrt{5}}{5}\). No. 5 * \(\frac{\sqrt{5}}{5}\) = \(\frac{\sqrt{5}}{1}\). The reciprocal of 5 is 1/5. The reciprocal of \(\frac{\sqrt{5}}{5}\) is \(\frac{5}{\sqrt{5}}\). Reject.

IMO, Answer

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Re: In the following pairs of numbers, which are reciprocals of each other  [#permalink]

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New post 24 Jun 2017, 08:56
Bunuel wrote:
In the following pairs of numbers, which are reciprocals of each other?

I. 1 and 1
II. 1/11 and −11
III. 5 and \(\frac{\sqrt{5}}{5}\)

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) II and III only


Reciprocals multiplied to each other will always be \(= 1\).

Lets check this rule on the options.

I. 1 and 1

\(1 * \frac{1}{1} = 1\) ---------- (Reciprocals)

II. \(\frac{1}{11}\) and −11

\(\frac{1}{11} * - 11 = -1\) --------- (Not reciprocals)

III. 5 and \(\frac{\sqrt{5}}{5}\)

\(5 *\) \(\frac{\sqrt{5}}{5}\) \(= \sqrt{5}\) ---------- (Not reciprocals)

I Only. Answer (A) ...
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Re: In the following pairs of numbers, which are reciprocals of each other  [#permalink]

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New post 24 Jun 2017, 09:39
A number is a reciprocal of another number, if the numbers can be represented as x and \(\frac{1}{x}\)
Lets look at the answer options,
I. 1 and 1 (These are reciprocal numbers)
II. 1/11 and −11 (Two numbers can never be reciprocal if they are of the opposite sign)
III. 5 and \(\frac{\sqrt{5}}{5}\)

Since 5 = \(\sqrt{5}*\sqrt{5}\)
\(\frac{\sqrt{5}}{5}\) = \(\frac{\sqrt{5}}{\sqrt{5}*\sqrt{5}}\) = \(\frac{1}{\sqrt{5}}\)

5 and \(\frac{\sqrt{5}}{5}\) are not reciprocals.
Hence Option A(I only) is the only option which has reciprocal numbers.
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Re: In the following pairs of numbers, which are reciprocals of each other  [#permalink]

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New post 14 Jul 2017, 13:18
Bunuel Could you please modify the answer? Seems to most of us the answer is A. If not, please provide an explanation. Thank you.
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Re: In the following pairs of numbers, which are reciprocals of each other   [#permalink] 14 Jul 2017, 13:18
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