51 is related to 256 by certain logic. Following the same logic, 53 is related to 266. To which of the following is 55 related, following the same logic? (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

Correct — A. Rule: output = 5 x input + 1.

51 gives 5 x 51 = 255, and 255 + 1 = 256
53 gives 5 x 53 = 265, and 265 + 1 = 266

55 gives 5 x 55 = 275, and 275 + 1 = 276, which is option (a).

Cross-check on the gap: the input rises by 2 and the output by 10, so the multiplier is 10 / 2 = 5. From 53 to 55 is another 2, so 266 + 10 = 276.

Why the others are wrong

• (b)
  213 — Reverse the rule: 213 - 1 = 212, and 212 / 5 = 42.4, not 55. 213 is also smaller than the 266 that the smaller input 53 already produced.
• (c)
  249 — Reverse the rule: 249 - 1 = 248, and 248 / 5 = 49.6, not 55. Like 213 it falls below 266, which a larger input cannot do under a rising rule.
• (d)
  290 — Reverse the rule: 290 - 1 = 289, and 289 / 5 = 57.8, not 55. 290 is 266 + 24, where the step from 53 to 55 is worth only +10.

A number analogy hands you two worked examples and asks for a third. Two examples are enough to fit a straight line: take the multiplier from the change, then the constant from either example.

Change: the inputs 51 and 53 differ by 2 while the outputs 256 and 266 differ by 10, so each unit of input is worth 5.

Constant: 5 x 51 = 255 against an output of 256, so add 1. The relation is 5n + 1, and it must be checked on the second example before it is used on the third.

Key facts

• The relation is output = 5 x input + 1.
• 5 x 51 + 1 = 256 and 5 x 53 + 1 = 266.
• A two-example analogy fixes both a multiplier and a constant.

Common traps

• Fitting the rule to the first pair alone and never testing it on the second.
• Reading the +10 jump in the output as the value of one unit of input rather than two.
• Splitting 55 into 5 and 5, which the NOTE forbids.

No directly related past PYQ was found.