A stout man joined a weight loss program at a newly opened fitness center. At…
2025
A stout man joined a weight loss program at a newly opened fitness center. At the end of every month, the decrease in his weight from the original weight was measured and recorded as 1, 3, 8, 20, 42, .... Although the man made a steadfast effort, the weighing machine showed an erroneous value once. What was that erroneous value?
- A.
32
- B.
18
- C.
42
- D.
20
Attempted by 6 students.
Show answer & explanation
Correct answer: D
This is a mixed-recurrence number series, where each term is generated from the one before it using the rule: next term = (previous term × 2) + k, with k increasing by 1 at every step (k = 1, 2, 3, 4, ...). To find an erroneous term in such a series, regenerate each term in order from the rule and compare it with the value given; the first mismatch is the erroneous entry.
Term 1 = 1 (the starting value of the series).
Term 2 = 1 × 2 + 1 = 3, which matches the given series.
Term 3 = 3 × 2 + 2 = 8, which matches the given series.
Term 4 = 8 × 2 + 3 = 19 by the rule, but the series shows 20 at this position — a mismatch.
Term 5, computed from the corrected Term 4 (19): 19 × 2 + 4 = 42, which matches the given series.
Because using the corrected value for Term 4 reproduces the given Term 5 exactly, the pattern is consistent everywhere except at Term 4. This confirms that 20 is the sole erroneous entry recorded by the weighing machine — it should have read 19.
