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Olympiad Test: Knowing Our Numbers - Class 6 MCQ


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20 Questions MCQ Test Mathematics (Maths) Class 6 - Olympiad Test: Knowing Our Numbers

Olympiad Test: Knowing Our Numbers for Class 6 2024 is part of Mathematics (Maths) Class 6 preparation. The Olympiad Test: Knowing Our Numbers questions and answers have been prepared according to the Class 6 exam syllabus.The Olympiad Test: Knowing Our Numbers MCQs are made for Class 6 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Knowing Our Numbers below.
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Olympiad Test: Knowing Our Numbers - Question 1

Find the smallest number which will leave remainder 5 when divided by 8, 12, 16 and 20.

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 1

LCM of 8, 12, 16, 20 is 240

240 is the smallest number when divided by 8, 12, 16 and 20 always leaves remainder equal to zero.

So, we have to add 5 to get 5 as remainder

⇒ 240 + 5 = 245

∴ 245 is the right answer

Olympiad Test: Knowing Our Numbers - Question 2

The product of two numbers is 2025 and their HCF is 15. What is their LCM?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 2

HCF × LCM = Product of numbers.
15 × LCM = 2025 
LCM = 2025 / 15 = 135.

Olympiad Test: Knowing Our Numbers - Question 3

If the number 2734 is divided by the sum of its digits, what is the remainder?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 3

The sum of the digits of 2734 is 2 + 7 + 3 + 4 = 16.
When 2734 is divided by 16, the remainder is 2734 mod 16 = 14.

Olympiad Test: Knowing Our Numbers - Question 4

If the number 12345 is multiplied by 99, what is the sum of the digits of the product?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 4

The product is 12345 × 99 = 1222155.
Sum of digits: 1 + 2 + 2 + 2 + 1 + 5 + 5 = 18.

Olympiad Test: Knowing Our Numbers - Question 5

What is the smallest 4-digit number divisible by 11?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 5

When 1000 is divided by 11, the remainder is 10, 
∴ 1001 is the smallest 4-digit number divisible by 11.

Olympiad Test: Knowing Our Numbers - Question 6

What is the largest 5-digit number divisible by 16, 24, and 36?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 6

LCM of 16, 24, and 36 is 144. Largest 5-digit number is 99936.

Olympiad Test: Knowing Our Numbers - Question 7

If the product of three consecutive numbers is 336, what is the middle number?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 7

For three consecutive numbers (n-1), n ,(n+1), their product is (n-1)(n)(n+1) = 336.
Checking for n = 7,
6 × 7 × 8 = 336.

Olympiad Test: Knowing Our Numbers - Question 8

If A is the smallest number such that 205 x A is a perfect square, what is A?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 8

The prime factorization of 205 is 5 × 41.
to make perfect square term should be even no of terms so 
To make it a perfect square, multiply by 41 x 7.
so that it would be 412 x 72

Olympiad Test: Knowing Our Numbers - Question 9

What is the sum of the first 50 even numbers?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 9

Sum of the first n even numbers is n(n+1).
Sum = 50 × 51 = 2550.

Olympiad Test: Knowing Our Numbers - Question 10
Which of the following is a prime number?
Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 10
61 is a prime number. 51 = 3 × 17, 57 = 3 × 19, 63 = 3 × 21.
Olympiad Test: Knowing Our Numbers - Question 11
What is the least common multiple (LCM) of 24, 36, and 54?
Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 11
LCM of 24, 36, and 54 is found by taking the highest powers of all prime factors:
24 = 2³ × 3, 36 = 2² × 3², 54 = 2 × 3³.
LCM = 2³ × 3³ = 216.
Olympiad Test: Knowing Our Numbers - Question 12
What is the value of
123456789
×
987654321
123456789
+
987654321
123456789+987654321
123456789×987654321

?
Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 12
The value simplifies using the formula for the product of sums and differences of two numbers.
Olympiad Test: Knowing Our Numbers - Question 13
What is the smallest number which when increased by 17 is exactly divisible by 12, 15, and 18?
Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 13
LCM of 12, 15, and 18 is 180. The number is 180k - 17. Smallest such k = 1, 180 - 17 = 163.
Olympiad Test: Knowing Our Numbers - Question 14

If 1234x5678 is divisible by 9, what is the value of x?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 14

Sum of digits: 1 + 2 + 3 + 4 + x + 5 + 6 + 7 + 8 = 36 + x.
For divisibility by 9, x must be 0.

Olympiad Test: Knowing Our Numbers - Question 15

If the difference between a number and its reciprocal is 24/5, what is the number?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 15

Let the number be x. Then, x - 1/x = 24/5.
check by putting values of x 
Solving for x, we get x = 5.

Olympiad Test: Knowing Our Numbers - Question 16

How many numbers between 1000 and 9999 are divisible by both 3 and 4?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 16

LCM of 3 and 4 is 12. Range: 1008, 1020, ... , 9996.
sum = (a + l)/2  a = first letter and l = last number
Count = (9996 - 1008)/12 + 1 = 750.

Olympiad Test: Knowing Our Numbers - Question 17

What is the smallest 5-digit number that can be expressed as the sum of two squares?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 17

10000 is a smallest 5 digit number 
10000 =1002
now smallest Square is 1 = 12
10001 = 100² + 1².

Olympiad Test: Knowing Our Numbers - Question 18
Which number is a perfect square and is the sum of three consecutive odd numbers?
Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 18
Check for perfect squares: 81 = 25 + 27 + 29.
Olympiad Test: Knowing Our Numbers - Question 19

The sum of three consecutive even numbers is 150. What is the largest of these numbers?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 19

Let the three consecutive even numbers be x, x+2, and x+4.
Sum: x + (x + 2) + (x + 4) = 3x + 6 = 150.
Solving for x: 3x = 144, x = 48.
The largest number is x + 4 = 52.

Olympiad Test: Knowing Our Numbers - Question 20

A 4-digit number is formed by repeating a 2-digit number. If the number is divisible by 7 and 13, what is the 2-digit number?

Detailed Solution for Olympiad Test: Knowing Our Numbers - Question 20

Let the 4-digit number be represented as 9191.
Such numbers can be represented as 101 times the 2-digit number.
Since the number is divisible by 7 and 13, it must be divisible by 91.
Checking 101 times 91 = 9191, which is divisible by both 7 and 13.
Hence, the 2-digit number is 91.

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