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Grade 5 AMO worksheet with math problems on reading, time, and scheduling.

A Grade 5 AMO worksheet with questions about books read by children, time calculations, and employee shifts, featuring a table and multiple-choice options.

A Grade 5 AMO worksheet with questions about books read by children, time calculations, and employee shifts, featuring a table and multiple-choice options.

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Show Answer Key & Explanations Step-by-step solution for: Grade 5 - American Mathematics Olympiad | Preparation, Online ...
Let's solve each problem step by step.

---

Problem (1):


The table below shows the number of books read by five children in one month.

| Name | Number of books |
|-----------|-----------------|
| Kiyoraka | ? |
| May | 19 |
| Alan | 10 |
| Syafiqah | 25 |
| Kim | 21 |

If Kiyoraka read 6 books more than \(\frac{1}{5}\) of the total number of books read by the other four children, then how many books did Kiyoraka read in a month?

#### Solution:
1. Calculate the total number of books read by the other four children:
\[
\text{Total for May, Alan, Syafiqah, and Kim} = 19 + 10 + 25 + 21 = 75
\]

2. Find \(\frac{1}{5}\) of this total:
\[
\frac{1}{5} \times 75 = 15
\]

3. Kiyoraka read 6 books more than this value:
\[
\text{Books read by Kiyoraka} = 15 + 6 = 21
\]

#### Answer:
\[
\boxed{21}
\]

---

Problem (2):


Ahmad's watch is not showing the correct time. When it was 04:40, his watch showed 04:25. He was to reach the station at 08:30 AM, but when he reached there his watch was showing 08:40 AM. Ahmad is late to the station by how many minutes?

#### Solution:
1. Determine the actual time when Ahmad's watch shows 08:40 AM:
- When the actual time is 04:40, Ahmad's watch shows 04:25.
- This means Ahmad's watch is running slow by:
\[
04:40 - 04:25 = 15 \text{ minutes}
\]
- Therefore, for every real hour, Ahmad's watch shows 45 minutes (since it loses 15 minutes per hour).

2. Calculate the actual time when Ahmad's watch shows 08:40 AM:
- The difference between 04:25 and 08:40 on Ahmad's watch is:
\[
08:40 - 04:25 = 4 \text{ hours } 15 \text{ minutes}
\]
- Since Ahmad's watch runs slow by 15 minutes per hour, we need to convert this into real time:
\[
\text{Real time elapsed} = \frac{4 \text{ hours } 15 \text{ minutes}}{45 \text{ minutes per hour}}
\]
- Convert 4 hours 15 minutes into minutes:
\[
4 \times 60 + 15 = 255 \text{ minutes}
\]
- Convert this back to real time:
\[
\text{Real time elapsed} = \frac{255}{45} \text{ hours} = 5 \text{ hours and } 30 \text{ minutes}
\]
- Add this to the actual time when Ahmad's watch showed 04:25:
\[
04:40 + 5 \text{ hours } 30 \text{ minutes} = 10:10 \text{ AM}
\]

3. Determine how late Ahmad is:
- Ahmad was supposed to reach the station at 08:30 AM, but he arrived at 10:10 AM.
- The delay is:
\[
10:10 - 08:30 = 1 \text{ hour } 40 \text{ minutes} = 100 \text{ minutes}
\]

#### Answer:
\[
\boxed{d}
\]

---

Problem (3):


\[
\triangle + \triangle + \triangle + \triangle + \triangle + \triangle = 96
\]
\[
\triangle + \heartsuit = 25
\]
Find the value of \(\triangle + \heartsuit + \heartsuit\).

#### Solution:
1. Solve for \(\triangle\):
\[
6\triangle = 96 \implies \triangle = \frac{96}{6} = 16
\]

2. Solve for \(\heartsuit\):
\[
\triangle + \heartsuit = 25 \implies 16 + \heartsuit = 25 \implies \heartsuit = 25 - 16 = 9
\]

3. Find the value of \(\triangle + \heartsuit + \heartsuit\):
\[
\triangle + \heartsuit + \heartsuit = 16 + 9 + 9 = 34
\]

#### Answer:
\[
\boxed{c}
\]

---

Problem (4):


There are 36 employees in a company, who work in three shifts. The first group of 9 employees work from 09:00 AM to 01:00 PM. The second group of 12 employees work from 11:00 AM to 02:00 PM. The third group of 15 employees work from 01:00 PM to 02:00 PM. If there are only 3 computers, during what time are the computers likely to be used most?

#### Solution:
1. Analyze the overlap of shifts:
- Shift 1 (09:00 AM to 01:00 PM): 9 employees
- Shift 2 (11:00 AM to 02:00 PM): 12 employees
- Shift 3 (01:00 PM to 02:00 PM): 15 employees

2. Determine the number of employees working at different times:
- From 09:00 AM to 11:00 AM: Only Shift 1 is working (9 employees).
- From 11:00 AM to 01:00 PM: Both Shift 1 and Shift 2 are working:
\[
9 + 12 = 21 \text{ employees}
\]
- From 01:00 PM to 02:00 PM: All three shifts are working:
\[
9 + 12 + 15 = 36 \text{ employees}
\]

3. Identify the time with the maximum number of employees:
- The maximum number of employees working simultaneously is 36, which occurs from 01:00 PM to 02:00 PM.

#### Answer:
\[
\boxed{b}
\]

---

Final Answers:


1. \(\boxed{21}\)
2. \(\boxed{d}\)
3. \(\boxed{c}\)
4. \(\boxed{b}\)
Parent Tip: Review the logic above to help your child master the concept of 5th grade math olympiad worksheet.
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