If K is the sum of reciprocals of the consecutive integers from 43 to 48, inclusive, then K is closest in value to which of the following?
A. 1/12
B. 1/10
C. 1/8
D. 1/6
E. 1/4
K = 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48.
Determine the RANGE of the sum.
The smallest fraction = 1/48.
If all of the 6 fractions were 1/48, the result would be the following sum:
6(1/48) = 1/8.
Since all but one of the fractions are actually GREATER THAN 1/48, the value of K must be GREATER THAN 1/8.
The greatest fraction = 1/43.
If all of the 6 fractions were 1/42, the result would be the following sum:
6(1/42) = 1/7.
Since all of the fractions are actually LESS THAN 1/42, the value of K must be LESS THAN 1/7.
Thus:
1/8 < K < 1/7.
Answer choices A and B are BELOW this range.
Answer choices D and E are ABOVE this range.
The correct answer is
C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
