NIMCET 2020 — Reasoning PYQ

Step 1: Find the differences between consecutive terms

Let us analyze the differences between adjacent numbers in the given series to identify the underlying pattern:

• $58-56=2$

• $62-58=4$

• $70-62=8$

• $84-70=14$

• $118-84=34$

• $182-118=64$

Step 2: Identify the logical mathematical pattern

Looking closely at the differences: $2,4,8,14,34,64$...

The numbers $2,4,8$, and $64$ strongly suggest a geometric progression based on powers of $2$ ($2^1,2^2,2^3,2^4,2^5,2^6$).

Let's test this ideal power-of-2 sequence for the differences:

• First difference: $2^1=2$

• Second difference: $2^2=4$

• Third difference: $2^3=8$

• Fourth difference should be: $2^4=16$

• Fifth difference should be: $2^5=32$

• Sixth difference should be: $2^6=64$

Step 3: Recalculate the series with the correct differences

Let's see what happens to the terms when we apply the correct differences starting after $70$:

• $56+2=58$ (Correct)

• $58+4=62$ (Correct)

• $62+8=70$ (Correct)

• $70+16=86$ (Instead of 84)

• $86+32=118$ (Matches perfectly with the next term!)

• $118+64=182$ (Matches perfectly with the final term!)

Since replacing $84$ with $86$ corrects the entire remainder of the sequence, 84 is undeniably the wrong number in this series.

Correct Option: C