2017 AMC 10A Real Questions and Analysis

In this article, you’ll find:

• Representative real questions from each module with detailed solutions.
• The complete 2017 AMC 10A Answer Key.
• The best resources to prepare effectively for the AMC 10.
• A concise topic distribution chart showing which areas appeared most in the 2017 AMC 10A.
• A module-to-question mapping table highlighting the core concepts tested in each module for the 2017 AMC 10A.

Real Question and Solutions Explained

Algebra Example – Problem 2

Question:

Pablo buys popsicles for his friends. The store sells single popsicles for $1 each, 3–popsicle boxes for $2 each, and 5–popsicle boxes for $3. What is the greatest number of popsicles that Pablo can buy with $8?

(A) 8 (B) 11 (C) 12 (D) 13 (E) 15

Solution:

Best value per dollar is the 5–pack \( \left( \frac{5}{3} \right) \), then the 3–pack \( \left( \frac{3}{2} \right) \), then singles \( \left( \frac{1}{1} \right) \).
Use as many 5–packs as possible: with $8 take two 5–packs ($6) and one 3–pack ($2).

Popsicles: \( 5 \cdot 2 + 3 = 13 \).

Any other combination gives at most 12 (e.g., four 3–packs, or one 5–pack + two 3–packs + one single).

Answer (D)

Common Mistakes:

• Forgetting that you must spend at most $8 exactly; some mixes leave unused money.
• Comparing packs by price instead of value per dollar.

Number Theory Example – Problem 16

Question:

There are 10 horses named Horse \(k\) that take exactly \(k\) minutes per lap. Starting together, the least time \(S>0\) when all 10 are simultaneously back at the start is \(S=2520\). Let \(T>0\) be the least time such that at least 5 of the horses are again at the starting point together. What is the sum of the digits of \(T\)?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

Solution:

At time \(t\), Horse \(k\) is at the start iff \(k\mid t\). We want the smallest \(t>0\) with at least 5 distinct \(k\in\{1,\dots,10\}\) dividing \(t\).

Check minimal \(t\):

• \(t=10\Rightarrow \{1,2,5,10\}\) → 4 horses.
• \(t=12\Rightarrow \{1,2,3,4,6\}\) → 5 horses (works).
  No smaller \(t\le 11\) has 5 divisors from \(\{1,\dots,10\}\).

Thus \(T=12\). Sum of digits: \(1+2=3\).

Answer (B)

Common Mistakes:

• Looking for 5 distinct lap times without divisor nesting (e.g., \(1,2,3,4,6\) all dividing 12).
• Thinking \(T\) must be one of the existing lap times.

Geometry Example – Problem 3

Question:

Tamara has three rows of two \(6\)-ft by \(2\)-ft flower beds. The beds are separated and surrounded by \(1\)-ft–wide walkways as shown. What is the total area of the walkways, in square feet?

(A) 72 (B) 78 (C) 90 (D) 120 (E) 150

Solution:

Overall outer rectangle: width \(=1+6+1+6+1=15\) ft; height \(=1+2+1+2+1+2+1=10\) ft.
Total outer area \(=15\times 10 = 150\).

There are \(6\) beds, each \(6\times 2 = 12\) sq ft, so total bed area \(=6\times 12 = 72\).

Walkway area \(=150 – 72 = 78\).

Answer (B)

Common Mistakes:

• Missing one of the outer/between \(1\)-ft strips.
• Treating \(6\times 2\) as orientation–independent without counting rows/columns.

Combinatorics Example – Problem 8

Question:

At a gathering of 30 people, 20 all know each other and 10 know no one. People who know each other hug; people who do not know each other shake hands. How many handshakes occur?

(A) 240 (B) 245 (C) 290 (D) 480 (E) 490

Solution:

The 20 mutual acquaintances produce 0 handshakes (they hug).
Each of the 10 who know no one shakes with all 20: \(10\cdot 20=200\).
Among those 10, none know each other, so they also shake with each other:

\[
\text{within the 10} = \frac{10!}{2!\,8!} = 45.
\]

Total handshakes \(=200 + 45 = 245\).

Answer (B)

Common Mistakes:

• Double–counting handshakes or mixing hugs with handshakes.
• Assuming the 10 “know no one” except among themselves.

2017 AMC 10A Answer Key

Question	Answer
1	C
2	D
3	B
4	B
5	C
6	B
7	A
8	B
9	C
10	B
11	D
12	E
13	D
14	D
15	C
16	B
17	D
18	D
19	C
20	D
21	D
22	E
23	B
24	C
25	A

Free Download: 2017 AMC 10A Problems & Solution

Download AMC 10 Mock Exam & Practice Pack

Download AMC 10 mock exams with full solutions, key AR/HR knowledge reviews, and daily practice sets — perfect for focused and efficient prep.

• Mock Exams: Timed practice with full explanations to build test readiness and review mistakes.
• Knowledge Points: Covers must-know Algebra, Geometry, and Number Theory concepts for AMC 10.
• Daily Practice: Sharpen accuracy and speed with high-frequency AMC-style problems.

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Last 10 Years AMC 10 Real Questions and Analysis

Think Academy provides in-depth breakdowns of the past decade of AMC 10 exams. Click below to explore:

• Year-by-year topic trend insights and concept distributions

• Real AMC 10 exams from the last 10 years

• Official answer keys

• Representative questions, detailed solutions, and common mistakes

AMC 10A	AMC 10B
2024 AMC 10A	2024 AMC10B
2023 AMC 10A	2023 AMC10B
2022 AMC 10A	2022 AMC10B
2021 AMC 10A	2021 AMC10B
2020 AMC 10A	2020 AMC10B
2019 AMC 10A	2019 AMC10B
2018 AMC 10A	2018 AMC10B
2017 AMC 10A	2017 AMC10B
2016 AMC 10A	2016 AMC10B

2017 AMC 10A Topic Distribution

The 2017 AMC 10A featured 25 questions to be completed in 75 minutes, emphasizing advanced problem-solving and proof-based reasoning skills.

Learn more about AMC 10 Format and Scoring Here: AMC 10 FAQ and Resources: Your Ultimate Guide

Detailed Module Analysis

Module	Question Numbers	What It Tests (Brief)
Algebra	1–5, 7, 9, 12, 13, 14, 17, 24	Basic operations, functions, coordinate geometry
Number Theory	16, 20, 25	GCD/LCM, divisibility
Geometry	3, 10, 11, 21, 22	Polygons, solids, circles
Combinatorics / Probability	6, 8, 15, 18, 19, 23	Counting and probability

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