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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Mental Maths

1. What is the smallest odd composite number?
2. What is the greatest prime number less than 100?
3. How many even numbers are there between 58 and 80?
4. How many composite numbers between 10 and 50 have digit 3?
5. How many prime factors does the greatest 2-digit number have?
6. Which is the largest number that divides the sum of any pair of consecutive odd numbers?

Brain Sizzlers

1. The product of primes also gives palindromes.
For Example:
17 × 19 = 323
7 × 11 × 13 = 1001
5 × 7 × 11 × 13 = 5005
7 × 11 × 13 × 17 × 19 = 323323
Can you find 5 such palindromes which are obtained by multiplying prime numbers?
2. Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones; the numbers
which are prime in this sequence are called fibonacci primes such as 2, 3, 5, 13, ..., find the next two fibonacci
prime numbers.
3. If the product 4864 × 9H2 is divisible by 12, where H stands for a digit, then what is the smallest value of H?
4. Find the HCF and LCM of the smallest perfect number and smallest odd composite number.
5. Is the HCF of 169, 221 and 630 a prime number? Justify your answer.

Life Skills
A photographer is hired to take group photographs of students of each class in a school.
He arranges the students along with teachers in rows for the picture. His arrangement has
l At most 40 people
l An equal number of people in each row
l A row consists of a minimum of 3 people and a maximum of 8 people.
1. There are 35 people in a class for a grouped photograph. What are the possible arrangements for them?
2. If 28 students and 4 teachers are to be photographed, what is the possible arrangement for them?
(a) 2 rows with 16 people (b) 4 rows with 8 people
(c) 5 rows with 6 students and 1 row for teachers
(d) 6 rows with 4 students in each and 1 row for teachers
3. The photographs are sold in small, medium and large sizes. The respective rates of photographs are shown
in the table below.
Photograph size Small Medium Large
Cost in ` 60 80 120
In all `10500 is collected for 140 photographs. There are 70 small-size photographs, 40 medium-size
photographs, and the rest large-size photographs. Is money sufficient to buy 140 photographs? Give your
reason.

167 Prime Time