Bunuel wrote:
For positive integers n, the integer part of the nth term of sequence A equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, A_1 = 1.2345678…, while A_2 = 2.4681012… The sum of the first seven terms of sequence A is between:
A. 28 and 29
B. 29 and 30
C. 30 and 31
D. 31 and 32
E. 32 and 33
Kudos for a correct solution.
MANHATTAN GMAT OFFICIAL SOLUTION:First, construct the first seven terms, though only out to a few decimal places, following the given pattern.
A_1 = 1.23…
A_2 = 2.46…
A_3 = 3.69…
A_4 = 4.812…
A_5 = 5.10…
A_6 = 6.12…
A_7 = 7.14…
Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.
1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3
Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.
The correct answer is C.
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