(1/21)+(1/22)+(1/23)+(1/24)+(1/25)+(1/26)+(1/27)+(1/28)+(1/2

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hazelnut01: Master | Next Rank: 500 Posts; Posts: 157; Joined: Sat Nov 19, 2016 5:34 amFollowed by: 4 members; Thanked: 2 times

by hazelnut01 » Thu May 11, 2017 10:52 pm

If a=(1/21)+(1/22)+(1/23)+(1/24)+(1/25)+(1/26)+(1/27)+(1/28)+(1/29)+(1/30). What is the value of a?

(A) 0.15 < a < 0.25
(B) 0.25 < a < 0.35
(C) 0.35 < a < 0.45
(D) 0.45 < a < 0.55
(E) 0.55 < a < 0.65

OA=C

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Source: Beat The GMAT — Problem Solving | Thu May 11, 2017 10:52 pm

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 » Fri May 12, 2017 3:33 am

ziyuenlau wrote:If a=(1/21)+(1/22)+(1/23)+(1/24)+(1/25)+(1/26)+(1/27)+(1/28)+(1/29)+(1/30). What is the value of a?

(A) 0.15 < a < 0.25
(B) 0.25 < a < 0.35
(C) 0.35 < a < 0.45
(D) 0.45 < a < 0.55
(E) 0.55 < a < 0.65

Determine the RANGE of the sum.
There are 10 fractions in total.
The smallest fraction is 1/30.
The greatest fraction is 1/21.

If all 10 fractions were 1/30, then a = 10(1/30) = 1/3 â‰ˆ 0.33.
Since 9 of the fractions are actually GREATER THAN 1/30, a must be GREATER THAN 0.33.

If all 10 fractions were 1/20, then 1 = 10(1/20) = 1/2 = 0.5.
Since all 10 fractions are actually LESS THAN 1/20, a must be LESS THAN 0.5.

Thus:
0.33 < a < 0.5.

Of the five answer choices, the closest match to the range in blue is C.

The correct answer is C.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri May 12, 2017 4:57 am

Here's a similar question to practice with: https://www.beatthegmat.com/m-is-the-sum ... 94397.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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