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AMC 10 PRMO USA Math Olympiad

Inequality (Forerunner Problem 2)

Problem – Inequality (Forerunner Problem 2)


The maximum number of passengers a bus can hold is 40. Which of the following is correct?

  • Passengers < 40
  • Passengers ≤ 40
  • Passengers > 40
  • Passengers ≥ 40

Key Concepts


Inequality

Mathematical Analysis

Number

Check the Answer


Answer: Passengers ≤ 40

Forerunner Problem Number 2 (Math is Fun)

Secrets in Inequalities.

Try with Hints


This problem is very easy to solve.We can start with a basic chart

Inequality- chart

I think now its quite clear from the above chart that what we have to do

If the maximum number of passengers a bus can hold is 40 then the expression will be like Passenger \(\leq 40 \) .So the number of passenger it van hold is either 40 or less than 40. So the second option is the correct option.

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AMC 10 USA Math Olympiad

Basic Inequality – Problem 1 (Forerunner Problem List)

Problem – Basic Inequality


To enter a junior writing competition you must be under 12 years old. Which of the following is correct?

  • Age < 12
  • Age ≤ 12
  • Age > 12
  • Age ≥ 12

Key Concepts


Inequality

Mathematical analysis

Numbers

Check the Answer


Answer: Age < 12

Basic Problems of Inequalities

Secrets in Inequalities.

Try with Hints


The basic rule for inequalities can be explained by some imaginary values ………..

basic inequality - solution

Its one of the easiest sum. Here we only have to find the relation between the perimeter of this sum.We have two different perimeter

  1. Age
  2. Limitation on age
  3. So can you try to find the relation between these two that mentioned in this sum. Try to find it …………………………………….

For this sum its mentioned that the age is under 12 that means the age is less than 12.

If we try to implement it in this sum we can express it as :

Age \( \leq 12 \)

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AMC 10 Australian Math Competition USA Math Olympiad

Statistics Problem – Australian Mathematics Competition, 2014

Problem No – 21 – Australian Mathematics Competition – 2014


Here is a problem based on Statistics from Australian Mathematics Competition, 2014.

In a competition between four people, Sally scored twice as many points as Brian and 30 points more than Corrie. Donna scored 50 points more than Brian. Which of the following statements is definitely true?

  • Sally won the competition.
  • Brian came last in the competition.
  • Donna won the competition.
  • Corrie beat Brian.
  • Sally and Donna together scored more than Brian and Corrie.

Key Concepts


Mathematical Analysis

Statistics

Arithmetic

Check the Answer


Answer: Sally and Donna together scored more than Brian and Corrie.

Australian Mathematics Competition – Upper Primary Division – 2014 – UP 21

Statistics 10th Edition – Robert S. Witte and John S. Witte

Try with Hints


For first hint we can use a table form with some possibilities :

statistics problem - solution

So in the previous hint from the table its clear that the 1st , 2nd and 4th options are not correct. Now if we go with the higher numbers like 90,100 etc then there will be a change with the values.Try to find it out using a table.

I guess you have noticed the differences in values let try to do that……

statistics problem - solution

So can understand from this table that the 3rd option is also not correct .

We are told that Sally scored 30 points more than Corrie and Donna scored 50 points more than Brian, and so together Sally and Donna always scored 80 points more than Corrie and Brian

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