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S is the sum of the reciprocals of the squares of the prime numbers between 19 and 41, exclusive. Which of the following is closest to
the value of S?
  • a)
    2 x 10-4
  • b)
    5 x 10-3
  • c)
    2.5 x 10-2
  • d)
    5 x 10-2
  • e)
    2 x 10-1
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
S is the sum of the reciprocals of the squares of the prime numbers be...
Given
Prime numbers between 19 and 41, exclusive = {23, 29, 31, 37}
To Find: The option that is closest to the value of S
Approach:
  1. We’ll use the principles of estimation to answer the question.
    1. Note that the 5 options are not very far – off in magnitude (for example, Options C and D are of the same order, 10 ). So, we’ll not approximate aggressively.
  • To be on the safer side, we can estimate the Upper Bounds and the Lower Bounds for the value of S, so that we can then mark the answer we get with absolute confidence (and not worry if our answer could be wrong because we approximated more aggressively than we should have)
Working out
  • Finding the Upper Bound for S
  • Note that just calculating the Upper Bound eliminates Options C – E
 
 
  • Finding the Lower Bound for S
 
  • Finding the correct answer
    • We’ve calculated above that 2.5*10-3 < S < 10*10-3
Looking at the answer choices, we see that the only option that satisfies this range is Option B
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