Question
Minsi
MATHEMATICS OLYMPIAD
ROUND ONE - LEVEL THRE (GRADES 10, 11 AND 12) -
Timet 60 Minutes (
A)
B)
C)
D)
E)
A) 0
B) 1
C) 4
D) 5
E) 6
The numbers
A) 60
B) 50
C) 40
D) 30
E) 20
In a ‘ninety nine’ shop, all items cost a number of rands and 99 cents. Susan spent R665, 76.
How many ltems did she buy?
A) 23
B) 24
C) 65
D) 66
E) 76
Mary has the same number of brothers as she has sisters. Ench one of her brothers has
A) 5
B) 7
C) 9
D) 11
E) 13
Which of the following is equivalent to
A)
B)
C)
D)
E)
A) 8
B) 7
C) 6
D) 5
E) 4
ROUND ONE - LEVEL THRE (GRADES 10, 11 AND 12) -
Timet 60 Minutes (
A)
B)
C)
D)
E)
A) 0
B) 1
C) 4
D) 5
E) 6
A) 60
B) 50
C) 40
D) 30
E) 20
How many ltems did she buy?
A) 23
B) 24
C) 65
D) 66
E) 76
A) 5
B) 7
C) 9
D) 11
E) 13
A)
B)
C)
D)
E)
A) 8
B) 7
C) 6
D) 5
E) 4
Ask by Coleman Mann. in South Africa
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
- A) 6
- E) 6
- E) 20
- D) 66
- B) 7
- A) 8
Solution
Let’s solve each of the problems step by step.
Problem 1: Which of these is the largest number?
We need to evaluate each option:
A)
B)
C)
D)
E)
Now, comparing the results:
- A = 6
- B = 4
- C = 5
- D = 5
- E = 0
The largest number is A) 6.
Problem 2: What is the ‘hundreds’ digit of
First, we calculate
The hundreds digit is the third digit from the right, which is 6.
Problem 3: Find
We can express
Substituting
Expanding this:
Multiplying through by
This simplifies to:
Rearranging gives:
Dividing by 2:
Now we can use the quadratic formula:
Since the discriminant is negative, we need to check our calculations. Let’s solve the equations directly instead.
From
Let’s solve the system of equations directly:
We can express
Substituting into the second equation:
This leads to a quadratic equation. Solving it will give us
After solving, we find
Problem 4: How many items did Susan buy?
Susan spent R665.76. Each item costs R99.99.
Let
Calculating
Since
If
If
Thus, the only feasible solution is 66 items.
Problem 5: How many children are in Mary’s family?
Let
From the problem:
-
- Each brother has
more sisters than brothers:
Substituting
Solving gives:
Thus,
Problem 6: How many two-digit numbers have remainder 1 when divided by 3 and remainder 2 when divided by 4?
Let
Using the Chinese Remainder Theorem, we can find the numbers that satisfy both conditions.
The two-digit numbers start from 10 to 99. The first number satisfying
Finding the common numbers, we can list them:
- The numbers are
.
Counting these gives us 8 valid numbers.
Summary of Answers:
- A) 6
- E) 6
- E) 20
- D) 66
- B) 7
- A) 8
Answered by UpStudy AI and reviewed by a Professional Tutor
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Math enthusiasts throughout history have celebrated the beauty of problem-solving, with notable early civilizations like the Babylonians and Egyptians laying the groundwork for algebra and geometry. They used sophisticated techniques, such as the base-60 system and geometric approaches, which inform modern mathematics. Olympiads, like the one you’re preparing for, continue this legacy, challenging thinkers to stretch their limits and explore creative solutions to complex problems.
If you’re looking to sharpen your problem-solving skills, a great tip is to always verify the rules of arithmetic. Remember, multiplication takes precedence over addition and subtraction! Common mistakes involve miscalculating these priorities, which can skew results. For instance, in expressions with both addition and multiplication, ensure you handle multiplication first, just like prioritizing tasks in life to avoid chaos!
