FoundationNumeric answerFree solution

Compute 48×5248 \times 52 in your head.

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

Show the answer and worked solution

Answer

24962496

Both numbers sit two away from 5050, one above and one below, so the product is a difference of squares: (50−2)(50+2)=502−22=2500−4=2496(50 - 2)(50 + 2) = 50^2 - 2^2 = 2500 - 4 = 2496. Whenever two factors are symmetric about a round number, this turns a two-digit multiplication into one square you know and one small subtraction. Spotting the midpoint is the whole skill; it takes about a second once it is a habit.

Worked solution

  1. Formula
    (a−b)(a+b)=a2−b2(a-b)(a+b) = a^2 - b^2
  2. Substitute
    (50−2)(50+2)(50-2)(50+2)
  3. Solve
    2500−42500 - 4
  4. =2496= 2496
  5. Answer
    24962496

Takeaway: Factors symmetric about a round number: square the midpoint, subtract the square of the gap.

Answer it in practice – your answer is marked and recorded.

Reported in interviews at

Optiver, SIG (Susquehanna), IMC Trading

More mental maths and numerical fluency questions

Compute 48 × 52 in your head. · QuantMax