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Two positive integers differ by 4, and sum of their reciprocals is 10/

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Joined: 08 Oct 2010
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WE 3: 10
Two positive integers differ by 4, and sum of their reciprocals is 10/  [#permalink]

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New post 26 Oct 2010, 01:40
3
00:00
A
B
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Difficulty:

  25% (medium)

Question Stats:

74% (01:17) correct 26% (01:48) wrong based on 80 sessions

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Two positive integers differ by 4, and sum of their reciprocals is 10/21. Then one of the numbers is

a) 3
b) 1
c) 5
d) 21
e) 28
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Re: Two positive integers differ by 4, and sum of their reciprocals is 10/  [#permalink]

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New post 26 Oct 2010, 02:53
There are several ways to solve this question:

Algebraic approach:

Let n be the smaller integer => 1/n + 1/(n+4) = 10/21
Solve for n => n=3. Hence, answer b) is correct.

Picking numbers:

Start with middle choice, i.e. 5
5 obviously cannot be the larger of the two integers as this would mean that the smaller integer would equal 1 (hence reciprocal also 1) and the sum of the reciprocals would exceed 10/21.
If 5 is the smaller of the two integers => 1/5 + 1/9 = 14/45. This is smaller than 10/21.

Next, choose 3 and 7 (because 12 and 28 would obviously make sum of the reciprocals too small) => 1/3 + 1/7 = 10/21. Hence, answer b) is correct.

Considering Least common multiple:

For the sum of the reciprocals of the integers to have the denominator 21 both numbers must be divisors of 21. This only holds true for answer choice b).
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Re: Two positive integers differ by 4, and sum of their reciprocals is 10/  [#permalink]

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New post 26 Oct 2010, 03:23
My take on this question - to solve it in the least time - is to make algebraic equation and then pick numbers.

If one number is n, the other is (n + 4).
Given 1/n + 1/(n+4) = 10/21
I look at the options and say that I need 21 as the denominator. 3 is given as an option. If 3 is one number, the other will be 7. Quickly substitute the values and confirm.

1/3 + 1/7 = 10/21

Note: In GMAT it is advisable to confirm your answer even if it seems pretty obvious. They like to put small little tricks to waylay you!
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Re: Two positive integers differ by 4, and sum of their reciprocals is 10/  [#permalink]

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New post 27 Oct 2010, 01:48
1/n + 1/(n+4) = 1/21 =====> n = 3
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Re: Two positive integers differ by 4, and sum of their reciprocals is 10/  [#permalink]

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New post 08 Jan 2019, 18:06
Hello!

Could someone please solve by the algebraic approach?

Kind regards!
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Re: Two positive integers differ by 4, and sum of their reciprocals is 10/ &nbs [#permalink] 08 Jan 2019, 18:06
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Two positive integers differ by 4, and sum of their reciprocals is 10/

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