What is 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56?

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Mon Jul 08, 2019 11:29 pm

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[GMAT math practice question]

What is 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56?

A. 3/5
B. 5/8
C. 7/8
D. 8/9
E. 9/10

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jul 09, 2019 3:48 am

Max@Math Revolution wrote:[GMAT math practice question]

What is 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56?

A. 3/5
B. 5/8
C. 7/8
D. 8/9
E. 9/10

1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56

= 1/2 + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) + (1/6 - 1/7) + (1/7 - 1/8)

= 1/2 + 1/2 - 1/8

= 1 - 1/8

= 7/8

The correct answer is C.

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Wed Jul 10, 2019 11:56 pm

=>

1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56
= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6) + 1/(6*7) + 1/(7*8)
= (1/1 – 1/2) + (1/2 – 1/3) + (1/3 – 1/4) + (1/4 – 1/5) + (1/5 – 1/6) + (1/6 – 1/7) + (1/7 – 1/8)
= 1/1 – 1/8 = 7/8

Therefore, C is the answer.
Answer: C

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