Mavensecurities·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Quant engineer screen at Maven Securities, basically one math puzzle and done. Short but the kind of question that'll make you feel dumb if you freeze up.

Questions Asked (1)

The pairwise sums of three real numbers a, b, c are 39, 48, and 51 (in some order). What is the largest of the three numbers?

Algorithms & Data Structures

Author's notes

Blanked for a second because I kept trying to assign the sums to specific pairs before setting up the algebra.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Let the pairwise sums be x = a+b, y = a+c, z = b+c. Solve the system of equations to find a, b, c in terms of x, y, z, then substitute the given values and identify the largest number. Alternatively, note that the sum of all pairwise sums is 2(a+b+c), so compute a+b+c and subtract each pairwise sum to get the individual numbers.

Pro tip: After solving, verify that the pairwise sums of your numbers match the given values in some order. This quick check catches arithmetic errors and demonstrates rigor.

1. Define variables

Let the pairwise sums be x = a+b, y = a+c, z = b+c, where x, y, z are 39, 48, 51 in some order.

2. Relate sums to individual numbers

Observe that (a+b) + (a+c) + (b+c) = 2(a+b+c). So compute the total sum S = a+b+c = (x+y+z)/2.

3. Solve for each number

Subtract each pairwise sum from S: a = S - (b+c) = S - z, b = S - y, c = S - x. This gives the three numbers directly.

4. Compute and identify largest

Plug in the given values: S = (39+48+51)/2 = 69. Then a = 69-51=18, b=69-48=21, c=69-39=30. The largest is 30.

5. Verify

Check that the pairwise sums of 18, 21, 30 are 39, 48, 51: 18+21=39, 18+30=48, 21+30=51. Correct.

Key Points to Mention

System of equations: a+b, a+c, b+c
Sum of pairwise sums equals 2(a+b+c)
Solving by subtracting each pairwise sum from the total sum
Order of pairwise sums is not fixed, so assign variables accordingly
Verification step to ensure consistency
Efficient mental math: total sum = 69, then subtract

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.