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Set K

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by r2kins » Sat Jul 16, 2011 7:57 pm

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Difficulty—

Set K consists of all fractions of the form x/(x+2) where x is a positive even integer less than 20. What is the product of all the fractions in Set K ?

a. 1/20
b. 1/10
c. 1/9
d. 1/2
e. 8/9
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by Anurag@Gurome » Sat Jul 16, 2011 9:21 pm
r2kins wrote:Set K consists of all fractions of the form x/(x+2) where x is a positive even integer less than 20. What is the product of all the fractions in Set K ?
As the fractions are of the form x/(x + 2) and x is positive even integer, the numerator of a fraction in the set will be equal to the denominator of the previous fraction and they will cancel each other. hence, the product will be 2/20 = 1/10

For a more detailed solution, let us write some of the fractions of the set K.
2/4, 4/6, 6/8..., 16/18 and 18/20

Hence, the product of all the fractions = (2/4)*(4/6)*(6/8)*...*(16/18*)(18/20) = 2/20 = 1/10

The correct answer is B.
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by mirantdon » Sun Jul 17, 2011 2:09 am
1/10
Just observe the numerator of the first term and the denominator of the last term
the rest cancel..
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by Scott@TargetTestPrep » Tue Oct 02, 2018 6:15 pm
r2kins wrote:Set K consists of all fractions of the form x/(x+2) where x is a positive even integer less than 20. What is the product of all the fractions in Set K ?

a. 1/20
b. 1/10
c. 1/9
d. 1/2
e. 8/9
Let's begin by writing out this product:

2/4 x 4/6 x 6/8 x 8/10 x 10/12 x 12/14 x 14/16 x 16/18 x 18/20

So we see that everything cancels except the numerator of the first fraction and the denominator of the last fraction.

Thus, the product of all the fractions in set K is 2/20 = 1/10.

Answer: B

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