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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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New post 08 Jun 2014, 00:45
1
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A
B
C
D
E

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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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New post 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)
72=8*9 (Consecutive) and hence your answer.
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New post 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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New post 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

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

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New post 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.

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

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New post 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.

That is Answer E.
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New post 06 Apr 2019, 23:25
Two consecutive integers have no common factor except 1.
If we subtract the reciprocals of two consecutive integer, Then we actually multiply them in the denominator. So, we want their product in the denominator.

again, if we subtract the reciprocals of two consecutive integer, their difference will be in the numerator, which will be always 1.

Only (E), satisfies both of the restrictions.
9*8=72 and 9-8=1

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Which of the following fractions can be written as the   [#permalink] 06 Apr 2019, 23:25
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