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In which of the following pairs are the two numbers...

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by swerve » Sat Dec 30, 2017 6:45 am
In which of the following pairs are the two numbers reciprocals of one another?

$$I.\ \ 15\ and \ -1/15$$
$$II.\ \sqrt{2}\ and\ \frac{\sqrt{2}}{2}$$
$$III.\ \ 4\ and\ \frac{1}{4}$$

A. I only
B. III only
C. I and II
D. II and III
E. I and III

The OA is D.

Please, can any expert explain this PS question for me? I'm not sure why that is the correct answer. I need your help. Thanks.
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by Brent@GMATPrepNow » Sat Dec 30, 2017 8:39 am
swerve wrote:In which of the following pairs are the two numbers reciprocals of one another?

$$I.\ \ 15\ and \ -1/15$$
$$II.\ \sqrt{2}\ and\ \frac{\sqrt{2}}{2}$$
$$III.\ \ 4\ and\ \frac{1}{4}$$

A. I only
B. III only
C. I and II
D. II and III
E. I and III
Some examples of reciprocals:
2 and 1/2
13 and 1/13
-8 and -1/8
2/3 and 3/2
x and 1/x
a/b and b/a

Okay, now let's examine the 3 statements....

I) 15 and -1/15
Since reciprocals MAINTAIN the same sign (positive or negative), 15 and -1/15 are NOT reciprocals
This means we can ELIMINATE A, C and E

IMPORTANT: Notice that the two remaining answer choices (B and C) both suggest that III is true.
So, it MUST be the case that III is true, which means we need not bother to check III

II) √2 and (√2)/2
Since (√2)(√2) = 2, we can rewrite (√2)/2 as follows:
Notice that (√2)/2 = (√2)/(√2)(√2) = 1/√2
At this point, we can see that = √2 and 1/√2 are, indeed, reciprocals.

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Sun Aug 25, 2019 5:44 pm
swerve wrote:In which of the following pairs are the two numbers reciprocals of one another?

$$I.\ \ 15\ and \ -1/15$$
$$II.\ \sqrt{2}\ and\ \frac{\sqrt{2}}{2}$$
$$III.\ \ 4\ and\ \frac{1}{4}$$

A. I only
B. III only
C. I and II
D. II and III
E. I and III

The reciprocal of 15 is 1/15; so 15 and -1/15 are not reciprocals of each other.

The reciprocal of √2 is 1/√2 = √2/2 (after rationalizing the denominator); so √2 and √2/2 are reciprocals of each other.

The reciprocal of 4 is 1/4; so 4 and 1/4 are reciprocals of each other.

Answer: D

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by rishab0507 » Tue Aug 27, 2019 5:36 am
this is a very good question as answer is given in disguised form to trick

1 : clearly not as its negative recipocal

II : $$\sqrt{2}$$ : Can be written as $$\sqrt{2}$$ /2 : by multiplying and divding num abd den by $$\sqrt{2}$$
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