Count Array Pairs Divisible by K
A hard-tier problem at 30% community acceptance, tagged with Array, Math, Number Theory. Reported in interviews at PayPal and 0 others.
Count Array Pairs Divisible by K is a hard-tier problem that PayPal has asked. With a 30% acceptance rate, it trips up candidates who don't recognize the modular arithmetic pattern. The naive approach (checking every pair) works on small inputs but times out on real data. The trick is preprocessing remainders and using the mathematical relationship between pairs and divisibility. If this problem hits your live assessment and you blank on the optimization, StealthCoder solves it invisibly, surfacing the working solution in seconds.
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Count Array Pairs Divisible by K is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Built by an Amazon engineer who realized the OA tests how well you memorized 200 problems, not how well you code.
Get StealthCoderThe core insight lives in number theory. You can't just iterate all pairs when n is large. Instead, compute each element's remainder mod k, then count how many pairs of remainders sum to k (or are both zero). The preprocessing step transforms an O(n^2) brute force into O(n) with a hash map. Most candidates either miss the modulo property entirely or implement it inefficiently by still checking all pairs. Common pitfall: forgetting that a pair (r1, r2) where r1 + r2 = k must be counted carefully if r1 = r2 (avoiding double-counting). This is where StealthCoder becomes the safety net if you hit a wall during the OA and need a tested, working implementation fast.
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Count Array Pairs Divisible by K recycles across companies for a reason. It's hard-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Built by an Amazon engineer who realized the OA tests how well you memorized 200 problems, not how well you code. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Count Array Pairs Divisible by K interview FAQ
Why does the naive O(n^2) approach fail?+
Brute force checking every pair works on test cases with n under 1000, but real OAs have constraints (often n up to 10^5 or more). O(n^2) becomes 10^10 operations, which times out. The problem requires you to recognize the modular arithmetic structure to drop to O(n).
What's the actual pattern I need to spot?+
Two numbers a and b are divisible by k if (a + b) % k = 0. This is equivalent to (a % k + b % k) % k = 0. By grouping numbers by their remainder mod k, you can count valid pairs in one pass with a hash map instead of checking all combinations.
Is this really asked by PayPal?+
Yes, PayPal has reported this problem. It's a filtering question for backend and systems roles. The 30% acceptance rate reflects that most candidates don't know the modular preprocessing trick and attempt brute force, which fails on performance.
How do I avoid double-counting pairs when remainder equals k/2?+
If a remainder r equals k minus itself (when k is even and r = k/2), you're counting the same remainder twice. For that remainder, the valid pair count is C(count, 2) = count * (count - 1) / 2, not count * count. Off-by-one mistakes here are common in live settings.
Which topics does this actually test?+
Number Theory (modular arithmetic and divisibility rules), Array (iteration and preprocessing), and Math (combinatorics for pair counting). It's not just coding; it's pattern recognition under time pressure, which is why the acceptance rate is so low.
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