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Which of the following fractions can be written as the difference of r

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

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New post 11 Nov 2016, 14:25
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Which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

A. 1/100
B. 1/121
C. 1/45
D. 1/56
E. 3/72

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

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New post 11 Nov 2016, 14:44
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stonecold wrote:
Which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

A. 1/100
B. 1/121
C. 1/45
D. 1/56
E. 3/72


Great question!

First, let x and x+1 be two consecutive integers.
So, 1/x and 1/(x+1) are the reciprocals.
So, their difference = 1/x - 1/(x+1)
To subtract these fractions we must find common denominators.
So, 1/x - 1/(x+1) = (x+1)/(x)(x+1) - x/(x+1)(x)
= 1/(x)(x+1)

Notice that the denominator is the product of two consecutive integers AND the numerator is 1
Check the denominators of the answer choices:
A. 1/100 We can't write 100 as the product of two consecutive integers. ELIMINATE.
B. 1/121 We can't write 121 as the product of two consecutive integers. ELIMINATE.
C. 1/45 We can't write 45 as the product of two consecutive integers. ELIMINATE.
D. 1/56 We CAN write 56 as the product of two consecutive integers (7x8). KEEP
E. 3/72 We CAN write 72 as the product of two consecutive integers (8x9). KEEP

We're left with D and E.
Since E is not in the correct format (with 1 in the numerator), we can ELIMINATE E
Answer:

ASIDE: 1/56 = 1/(7)(8) = 1/(x)(x+1)
So, x = 7 and x+1 = 8
Notice that 1/7 - 1/8 = 8/56 - 7/56 = 1/56!

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

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New post 11 Nov 2016, 14:48
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stonecold wrote:
Which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

A. 1/100
B. 1/121
C. 1/45
D. 1/56
E. 3/72



=1/n - 1/(n+1)

=1/n(n+1)

Only answer choice that satisfies above equation is D

1/7*8


D


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

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New post 11 Nov 2016, 22:16
stonecold wrote:
Which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

A. 1/100
B. 1/121
C. 1/45
D. 1/56
E. 3/72
Must be D. 1/56 since 56=7x8. The difference will be of the form 1/a X (a+1)


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

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New post 20 Aug 2018, 23:58
stonecold wrote:
Which of the following fractions can be written as the difference of reciprocals of two consecutive integers?

A. 1/100
B. 1/121
C. 1/45
D. 1/56
E. 3/72



This is how I solved

let The no be x and x+1 .
Which means the reciprocals = 1/x + 1/( X+1) which also means 2 consecutive integer should add upto the no.

Check ans choice and see which no is the multiplication of two consecutive nos
eg : a) 100 = 10 * 10 so rule out
c) 45 = 7*6 = 42+3 so rule out
d) 56 = 7*8 = 56 keep
e) 72 = 9*8 = keep

We're left with D and E.
Since E is not in the correct format (with 1 in the numerator), we can ELIMINATE E
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Re: Which of the following fractions can be written as the difference of r &nbs [#permalink] 20 Aug 2018, 23:58
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