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Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Which of the following pairs of integers have reciprocals whose sum is  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 65% (01:48) correct 35% (02:02) wrong based on 74 sessions

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Which of the following pairs of integers have reciprocals whose sum is either less than $$\frac{1}{3}$$ or greater than $$\frac{1}{2}$$?

I. 1 and 14
II. 5 and 10
III. 7 and 8

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

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Director  V
Status: Manager
Joined: 27 Oct 2018
Posts: 816
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: Which of the following pairs of integers have reciprocals whose sum is  [#permalink]

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for (I), it is clear that the sum is $$>\frac{1}{2}$$ because the reciprocal of 1 is 1 --> yes

for (II), $$\frac{2}{10}+\frac{1}{10} = \frac{3}{10}$$ $$= 0.3 < 0.3333 = \frac{1}{3}$$ --> yes

for (III), $$\frac{1}{7}+\frac{1}{8} = \frac{7+8}{56} = \frac{15}{56}$$ --> 15 is less than third 56 so $$<\frac{1}{3}$$ --> yes

E
CrackVerbal Quant Expert G
Joined: 12 Apr 2019
Posts: 362
Re: Which of the following pairs of integers have reciprocals whose sum is  [#permalink]

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For this question we start off by taking the fraction equivalents of decimals and see which statements satisfy the conditions given.
We also keep in mind that one of the conditions needs to be satisfied – either less than 1/3 or more than 1/2. Clearly, it cannot be both, right?

1.3 = 0.3333.. and ½ = 0.50. So, the sum of the reciprocals should be less than 0.33 or more than 0.50.

The integers in statement I are 1 and 14. Reciprocals of these integers are 1 and 1/14 respectively. 1/14 = 0.0714… The sum of these values = 1.0714. This is definitely more than 0.50. Statement I has to be a part of the answer. So, answer options B and C can be eliminated.

The integers in statement II are 5 and 10. Reciprocals of these integers are 1/5 and 1/10 respectively. 1/5 = 0.20 and 1/10 = 0.10, which add up to 0.30. This is less than 0.33. Statement II is also true. Answer option A can be eliminated.

The integers in statement III are 7 and 8. Reciprocals of these integers are 1/7 and 1/8. 1/7 = 0.1428 and 1/8 = 0.125. Adding these two will give us a sum less than 0.33. Statement III is also true, based on which answer option D can be eliminated.
The correct answer option is E.

Questions like these test your calculation skills, so it makes sense to work on honing them so that you are quick in answering these sort of questions.

Hope that helps!
_________________ Re: Which of the following pairs of integers have reciprocals whose sum is   [#permalink] 16 Dec 2019, 23:37
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# Which of the following pairs of integers have reciprocals whose sum is  