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 ≈ 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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