AMC 8 · 2016 · #1

Grade 4 arithmetic

Archetype Arithmetic Expression Decomposition └ Sub-archetype Fraction / Expression Sum Evaluation

unit-conversionmulti-digit-arithmetic dimensional-analysisidentify-subproblems ↑ Prerequisites: multi-digit-arithmetic

📏 Short solution 💡 2 insights

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Problem

A tennis match lasted 11 hours and 5 minutes. Express that total duration entirely in minutes.

Pick an answer.

(A)

605

(B)

655

(C)

665

(D)

1005

(E)

1105

AMC 8 2016 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Analyze the Units

The problem mixes two time units (hours and minutes) and asks for a single unit (minutes). Tool #8 (Analyze the Units) is the natural fit: convert hours to minutes using the rate 60 min/hr so every quantity is in the same unit before adding. Tool #7 (Identify Subproblems) is the matching habit — split the total into "minutes coming from the 11 hours" and "the extra 5 minutes", solve each, then combine.

1STEP 1

Split it into two pieces — the 11 hours and the leftover 5 minutes — convert each to minutes, then add.

11 hr + 5 min ⟶ (minutes from 11 hr) + 5 min

2STEP 2

Since 1 hour = 60 minutes, 11 × 60 = 660 minutes; the unit turns from hours into minutes.

11 hr × 60 min/hr = 660 min

3STEP 3

Add the leftover 5 minutes to 660, giving 665 minutes — choice (C).

660 min + 5 min = 665 min → (C)

Answer

665

An hour is 60 minutes, so 11 hours alone should be a bit over 600 minutes. 11 × 60 = 660 is in that range, and adding the small extra 5 minutes gives 665 — clearly between (A) 605 and (D) 1005. Choice (A) 605 would be the trap if you accidentally used 55 instead of 60 minutes per hour (11 × 55 = 605). Choice (E) 1105 is what you get from concatenating the digits "11" and "05" instead of computing — a written-form trap. 665 is the only value consistent with the actual minute-per-hour rate.

💡Key takeaway

This AMC 8 problem only needs Grade 4 unit conversion — once you turn hours into minutes, it's just addition.

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