If K is the sum of the reciprocals of the consecutive integers from 43 to 48, inclusive, then K is closest in value to which of the following?

Answer Choices

Correct answer marked below

1/12

1/10

1/8

Correct

1/6

1/4

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Comments

NeelamMay 22

This one had me stuck for a minute. I started adding them up directly and got lost in the fractions. Then I realized you can use the fact that all six numbers are around 45, so the sum is roughly 6/45 = 2/15. But 2/15 is about 0.133, and 1/8 is 0.125, so that's closest. Is that the right way to think about it?

JivagoJun 4

Yeah, that's a good approach. The actual sum is a bit less than 6/45 because the reciprocals of the larger numbers pull it down a bit, but it's still closest to 1/8.

HuanJun 4

I did the same but then checked with the first and last terms: 1/43 ≈ 0.0233 and 1/48 ≈ 0.0208, average ≈ 0.022, times 6 ≈ 0.132. Still points to 1/8.

RohanJul 9

I got 1/8 but I wasn't sure if I should pick the closest. The exact sum is about 0.132, and 1/8 is 0.125, 1/6 is about 0.166, so 1/8 is closer. But is there a faster way without calculating?

ArinJul 18

You can bound it: the sum is between 6/48 = 1/8 and 6/43 ≈ 0.1395. Since 0.1395 is closer to 0.125 than to 0.166, it's 1/8. But you still need to check.

AlbertoAug 4

I thought this was a bit tricky because the answer choices are 1/12, 1/10, 1/8, 1/6, 1/4. I initially guessed 1/6 because 6/45 = 2/15 ≈ 0.133, and 1/6 is 0.166, but 1/8 is 0.125. So 1/8 is closer. Good reminder to always compare decimals.

NurmuhammadSep 14

Nice question! I like how it forces you to estimate rather than compute exactly. The key is recognizing that the sum is approximately 6 divided by the average of the numbers, which is about 45.5.

What this question tests

What it tests

Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.

Common trap

Applying the order of operations out of sequence or rounding intermediate values before the final step.