Set K

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r2kins: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Sat Apr 17, 2010 7:30 am; Thanked: 2 times

by r2kins » Sat Jul 16, 2011 7:57 pm

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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Source: Beat The GMAT — Problem Solving | Sat Jul 16, 2011 7:57 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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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mirantdon: Master | Next Rank: 500 Posts; Posts: 135; Joined: Thu May 05, 2011 9:00 amFollowed by: 1 member; Thanked: 4 times; GMAT Score:700

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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