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Re: If the sum of the reciprocals of two consecutive odd integers [#permalink]

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25 Jul 2017, 09:39

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This post was BOOKMARKED

carcass wrote:

If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

A. 3

B. 5

C. 7

D. 9

E. 11

\(x = 5\) & \(y = 7\)

\(\frac{1}{x} + \frac{1}{y} = \frac{1}{5} + \frac{1}{7}\) = \(\frac{12}{35}\) Thus, the greater of the two integers is 7 answer must be (C) 7 _________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

A. 3

B. 5

C. 7

D. 9

E. 11

We can let the first odd integer = x and the next odd integer = x + 2; thus, the reciprocals are 1/x and 1/(x + 2). Thus:

1/x + 1/(x+2) = 12/35

Multiplying by 35x(x+2), we have:

35(x + 2) + 35x = 12x(x + 2)

35x + 70 + 35x = 12x^2 + 24x

12x^2 - 46x - 70 = 0

6x^2 - 23x - 35 = 0

(6x + 7)(x - 5) = 0

Thus, x = -7/6 or x = 5.

Since x is an integer, x must be 5 and the greater integer is x + 2 = 7.

Alternate solution:

We are given that the sum of the reciprocals of two consecutive odd integers is 12/35. We see that the denominator is 35. It’s not difficult to conjecture that the integers have to be 5 and 7 since 5 x 7 = 35. Finally, we can check the sum of 1/5 and 1/7 to see if they sum to 12/35:

1/5 + 1/7 = 7/35 + 5/35 = 12/35

Since they do add up to 12/35, the larger integer is 7.

Answer: C
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

A. 3

B. 5

C. 7

D. 9

E. 11

Since the denominator of the sum is 35, and since 35 equals the product of 5 and 7 (two consecutive odd integers), let's start by testing whether 5 and 7 are the integers in question.

So, the RECIPROCALS are 1/5 and 1/7 1/5 + 1/7 = 7/35 + 5/35 = 12/35 Voila!!

So, the odd integers are 5 and 7 The greater of the two integers is 7 Answer:

We're told that the sum of the reciprocals of two CONSECUTIVE ODD integers is 12/35. We're asked for the GREATER of the two integers. This question can be solved by TESTing THE ANSWERS.

Let's TEST Answer B: 5 IF.... the values are 3 and 5.... then the sum of the reciprocals is 1/3 + 1/5 = 5/15 + 3/15 = 8/15 This is clearly not the correct answer, but the denominator ends in a '5', so it's likely that 12/35 will ALSO include a 5...

Let's TEST Answer C: 7 IF.... the values are 5 and 7.... then the sum of the reciprocals is 1/5 + 1/7 = 7/35 + 5/35 = 12/35 This is an exact match for what we were told, so this MUST be the answer.