If 4 x 6 = 1812, 5 x 8 = 2415, 6 x 9 = 2718, then 7 x 6 =

The answer is A) 1821. Each product is written as two numbers, and both are multiples of 3. In 4 x 6 = 1812, the first part is 3 x 6 = 18 and the second part is 3 x 4 = 12. Check 5 x 8 = 2415: 3 x 8 = 24 and 3 x 5 = 15. Check 6 x 9 = 2718: 3 x 9 = 27 and 3 x 6 = 18. The rule is that the first number is multiplied by 3 to form the left part, and the second number is multiplied by 3 to form the right part. Applying this to 7 x 6, we get 3 x 6 = 18 and 3 x 7 = 21, so the answer is 1821.

• B) 2428 fits the pattern for neither part. 2428 would need 24 = 3 x 8, which matches only the second number of the question, not the first.
• C) 3035 uses 30 and 35, which are not multiples of 3 of the given numbers (3 x 10 and 3 x 11.67).
• D) 3642 reads as 36 and 42, which would need 3 x 12 and 3 x 14, so it does not follow from 6 and 7.

The core concept is pattern recognition in number series and coded arithmetic, which is a recurring reasoning theme in UPPSC Prelims. Test each hypothesis against all three given examples before accepting it.

Trap: Aspirants often try to find a pattern using addition or the product itself (4 x 6 = 24, 5 x 8 = 40) and get stuck. Splitting the four-digit output into two pairs and testing a multiplier against every example is the faster route.