Intelligent Math Puzzle – Challenge 79
Intelligent Math Puzzle – Challenge 79 gives four fractions in a sequence and asks for the fifth. Both the numerators and the denominators follow the same rule, so the puzzle is solved once you spot what that single rule is.
Challenge:
In the series 3/5 → 11/9 → 43/75 → 171/299 → ?, what is the fifth fraction?
A. 191/480
B. 513/897
C. 676/1199
D. 683/1195
E. 689/1211
The Answer
The correct answer is D. 683/1195.
Each term is built from the one before it by multiplying by 4 and subtracting 1, applied to the numerator and the denominator separately.
Numerators: 3 → 4(3) − 1 = 11 → 4(11) − 1 = 43 → 4(43) − 1 = 171 → 4(171) − 1 = 683.
Denominators: 5 → 4(5) − 1 = 19 → 4(19) − 1 = 75 → 4(75) − 1 = 299 → 4(299) − 1 = 1195.
So the fifth fraction is 683/1195.
One note on the puzzle image: the second fraction is printed as 11/9. For the pattern to hold it should read 11/19, since 4(5) − 1 = 19 and 4(19) − 1 = 75. Every other link in the chain follows the rule exactly.
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