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

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Difficulty:   15% (low)

Question Stats: 75% (00:42) correct 25% (00:42) wrong based on 81 sessions

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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

Source: Nova GMAT
Difficulty Level: 600

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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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.

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

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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)

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

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