Amazon·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Apr 2026

Summary

Got a math/logic question at Amazon that looks deceptively simple until you actually think about it. Short interview, one question, felt more like a quick screen than anything serious.

Questions Asked (1)

Which is greater: log(120) or log(1) + log(2) + log(3) + log(4) + log(5)?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

Blanked for a second because I was expecting a coding problem.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

First, recognize that the sum of logs equals the log of the product: log(1) + log(2) + log(3) + log(4) + log(5) = log(120). Then, since both sides are log(120), they are equal. Alternatively, compute the product 1*2*3*4*5 = 120 and compare directly.

Pro tip: Mention that this relies on the logarithmic identity log(a) + log(b) = log(ab), and note that the base of the logarithm doesn't matter as long as it's consistent. This shows you understand the underlying mathematical property and can generalize.

1. Identify the logarithmic identity

Recall that the sum of logarithms of numbers equals the logarithm of their product: log(a) + log(b) = log(ab).

2. Apply the identity to the right side

Combine the sum on the right: log(1) + log(2) + log(3) + log(4) + log(5) = log(1*2*3*4*5).

3. Compute the product

Calculate 1*2*3*4*5 = 120. So the right side simplifies to log(120).

4. Compare the two expressions

Both sides are log(120), so they are equal. Therefore, neither is greater; they are the same.

Key Points to Mention

The logarithmic identity: log(a) + log(b) = log(ab)
The product of 1 through 5 is 120 (i.e., 5! = 120)
The base of the logarithm is irrelevant for the comparison as long as it's consistent
The equality holds for any base (e.g., base 10, base e, base 2)
This is a straightforward application of logarithm properties, not requiring numerical approximation
Generalization: the sum of logs of the first n positive integers equals log(n!)

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