AMC 2023: Australian Mathematics Competition 2023 – Upper Primary, Solution

Let's discuss a problem from the AMC 2023 Upper Primary: Problem 17 which revolves around basic counting.

Problem

There are \(10\) questions in a test. Each correct answer scores \(5\) points, each wrong answer loses \(3\) points, and if a question is left blank it scores \(0\) points. Tycho did this test and scored \(27\) points. How many questions did Tycho leave blank? (amc-2023-17)

• (A) 1
• (B) 2
• (C) 3
• (D) 4
• (E) 5

Solution

From the given data we understand,

• For each correct answer, we get = \(+5\)
• And for each wrong answer,r we get = \(-3\)
• And for non-attempted questions, we get = \(0\)

Suppose one corrects all the questions then he will get = \( 10 \times 5 = 50\).

But Tycho got \(27\) marks so he couldn't correct all the questions. Some of them are wrong and some of them are un attempted along with the corrected answers.

Let's consider that he could solve correctly \(7\) problems so he will get: \(7 \times 5 = 35\)

He got wrong in \(2\) questions = \( 2 \times -3 = -6\)

He wasn't attempted \(1\) problem = \( 1 \times 0\)

Thus the total mark is: \( 35 - 6 + 0 = 29\) which does not match the desired marks.

Let's try with \(6 \)corrected problems = \( 6 \times 5 = 30\)

\(1\) incorrect problem = \(1 \times -3 = -3\)

And \(3\) unattempted questions = \( 3\times 0 = 0\)

Total marks he gets =\(30 - 3 + 0 = 27\).

So the number of unattempted questions is = C) \(3\).

What is AMC (Australian Mathematics Competition)?

The Australian Mathematics Competition (AMC) is one of the largest and oldest annual mathematics competitions in Australia, aimed at fostering interest and excellence in mathematics among students