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Re: Which of the following fractions can be written as the difference of r
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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:
Re: Which of the following fractions can be written as the difference of r
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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
gmatclubot
Re: Which of the following fractions can be written as the difference of r
[#permalink]
20 Aug 2018, 23:58