Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number: 3 : 30 :: 4 : 68 :: 5 : ?

Correct — C.
Rule: second number = n³ + n, where n is the first number.

3 → 3³ + 3 = 27 + 3 = 30 ✓
4 → 4³ + 4 = 64 + 4 = 68 ✓

5 → 5³ + 5
= 125 + 5 = 130 → option (c).

Why the others are wrong

• (a)
  175 — 175 is 125 + 50. The rule adds the number itself to its cube, and for 5 that is 125 + 5 = 130.
• (b)
  145 — 145 is 125 + 20. The pairs add 3 to 27 and 4 to 64, so for 5 the addition is 5, not 20.
• (d)
  126 — 126 is 5³ + 1. That rule would turn 3 into 28 and 4 into 65, not 30 and 68.

A number analogy hides one operation that turns the first number into the second. When the second is far bigger, try powers: 30 and 68 sit just above 27 and 64, the cubes of 3 and 4.

The amounts above the cubes, 3 and 4, are the numbers themselves, so the rule is n³ + n. It also reads as n × (n² + 1): 3 × 10, 4 × 17, 5 × 26 = 130.

Key facts

• 3³ = 27, 4³ = 64, 5³ = 125.
• n³ + n gives 30, 68 and then 130.
• The same values come from n × (n² + 1): 3 × 10, 4 × 17, 5 × 26.

Common traps

• Reading 4 : 68 as 4 × 17 and carrying ×17 over, which gives 51 for 3, not 30
• Adding 1 to the cube, which gives 28 for 3, not 30

No directly related past PYQ was found.