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# Which of the following fractions can be written as the

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Which of the following fractions can be written as the  [#permalink]

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08 Jun 2014, 00:45
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Which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72

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Re: Which of the following fractions can be written as the  [#permalink]

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08 Jun 2014, 01:25
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MensaNumber wrote:
which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

a) 1/24
b) 7/30
c) 1/45
d) 13/56
e) 1/72

Let the 2 consecutive integers be "a" and "a+1"

So we have $$\frac{1}{a}$$ - $$\frac{1}{(a+1)}$$

Simplify and we get $$\frac{1}{a(a+1)}$$....So the answer needs to have 1 in numerator and denominator should be product of consecutive integers...

Option B and D can be ruled out

24=6*4 (Not consecutive)
45= 9*5 (not consecutive)
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Which of the following fractions can be written as the  [#permalink]

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13 Sep 2014, 08:35
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We can represent two consecutive numbers as n and n+1
Where n < n+1

Reciprocate them = $$\frac{1}{n}> \frac{1}{n+1}$$

Subtract small from big..

$$\frac{1}{n} - \frac{1}{n+1}$$
$$\frac{1}{n^2+n}$$

So we must have 1 in numerator and denominator term can can be expressed in the from of n^2+1.

5 + 25 = 30
6+ 36 = 42
7+ 49 = 56
8 + 64 = 72 <<< matched << we have one answer choice (E) with 72 in denominator.
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Re: Which of the following fractions can be written as the  [#permalink]

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13 Sep 2014, 08:48
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Difference of reciprocals means 1 has to be in the numerator;

So option B & D can be ignored

For option A, B & E, we require to search two consecutive numbers whose product is the denominator

24 = 4 * 6 ......... Ignore

45 = 5 * 9 ........ Ignore

72 = 8 * 9 ................ Answer

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Re: Which of the following fractions can be written as the  [#permalink]

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13 Sep 2014, 10:56
let a and b be the consecutive integers.
1/b-1/a=(a-b)/ab

inverse of (a-b)/ab can be compared with inverse of each option

option 1 : ab/(a-b) = 24/1 .... no consecutive numbers have product as 24
option 2 : ab/(a-b) = 30/7.... denominator has to be 1 as a and b are consecutive numbers
option 3 : ab/(a-b) = 54/1 ..... no consecutive numbers have product as 54
option 4 : ab/(a-b) = 56/13 .... denominator has to be 1 as a and b are consecutive numbers
option 5 : ab/(a-b) = 72/1 ..... 8 & 9 satisfy the equation.

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Which of the following fractions can be written as the  [#permalink]

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21 Oct 2017, 13:01
NoHalfMeasures wrote:
Which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

A. 1/24
B. 7/30
C. 1/45
D. 13/56
E. 1/72

Look only at the denominators to start.

Which denominators are a product of two consecutive integers?

B) 7/30 (5*6 = 30)

D) 13/56 (7*8 = 56)

E 1/72 (8*9 = 72)

Now numerators. There is only one choice: a numerator of 1. The difference between two consecutive integers is 1.
(9-8) = 1.

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