Select the option in which the numbers share the same relationship as that shared by the given pair of numbers. (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.) 4 : 32 7 : 98

Correct — D. Both printed pairs double the square of the first number.

Rule: n → 2n².

4 : 4² = 16, then 16 × 2 = 32
7 : 7² = 49, then 49 × 2 = 98

Testing option (d): 3² = 9, then 9 × 2 = 18

So 3 : 18 carries the same relation, option (d).

Why the others are wrong

• (a)
  12 : 144 — 12 → 2 × 144 = 288. The printed 144 is 12², the square with the doubling left out.
• (b)
  10 : 1000 — 10 → 2 × 100 = 200. The printed 1000 is 10³, a cube where the rule wants twice a square.
• (c)
  8 : 192 — 8 → 2 × 64 = 128. The printed 192 is 3 × 64, so this option triples the square instead of doubling it.

A number-pair analogy has one rule, and two worked pairs are enough to pin it down. Test the simple families in order: n + k, n × k, n², n³, then combinations such as 2n² or n² + n.

Here 4 → 32 kills n + k and kills n² on its own, while 7 → 98 confirms 2n².

The wrong options are built from the neighbouring rules — n², n³ and 3n² — so a candidate who fixes the rule from one printed pair can land on any of them.

Key facts

• 2n² for small n: 3 → 18, 4 → 32, 5 → 50, 7 → 98, 8 → 128.
• Two worked pairs are printed precisely so that one rule survives and its near neighbours do not.
• 4 : 32 also fits n × 8, which is why the second pair 7 : 98 is needed to reject it.

Common traps

• Fixing the rule from one printed pair and skipping the second
• Reading 4 : 32 as n × 8 — true of that pair, false of 7 : 98
• Squaring correctly and then forgetting the doubling

No directly related past PYQ was found.