CAT 2025 Lesson : Class Discussion: Numbers - Factors & Remainders: 1 to 8

Class Discussion - Factors & Remainder

Question 1

It was Tina's birthday, and she was throwing a party for her friends. She bought 120 Kit Kat, 192 Perk and 144 5-Star chocolates to give her friends as return gifts. Each friend got the same number of Kit Kat, the same number of Perk and the same number of 5-Star chocolates. What is the least number of chocolates received by each of Tina's friends if she was left with no chocolates after the distribution?

		12
		19
		23
		24

Question 2

Maria, Thomas and Joanne run at constant speeds around a circular track and it takes them

6 \dfrac{2}{3}

4 \dfrac{1}{6}

and

4 \dfrac{4}{9}

minutes respectively to complete a lap. If they start running around the track at 4:00pm, when do all three meet at the start point for the first time?

		4:45:00 pm
		4:53:20 pm
		5:06:40 pm
		5:12:00 pm

Question 3

Three Vice Presidents (VP) regularly visit the plant on different days. Due to labour unrest, VP (HR) regularly visits the plant after a gap of 2 days. VP (Operations) regularly visits the plant after a gap of 3 days. VP (Sales) regularly visits the plant after a gap of 5 days. The VPs do not deviate from their individual schedules. CEO of the company meets the VPs when all the three VPs come to the plant together. CEO is on leave from January 5th to January 28th, 2012. Last time CEO met the VPs on January 3, 2012. When is the next time CEO will meet all the Vps?
[XAT 2012]

		February 6, 2012
		February 7, 2012
		February 8, 2012
		February 9, 2012
		None of the above

Question 4

How many factors of

p^{8} \times q^{12} \times r^{15}

are perfect squares or perfect cubes, where p, q and r are prime numbers?

Answer: 352

Question 5

How many numbers less than 500 have exactly 3 factors?

Answer: 8

Question 6

How many common factors exist for 504 and 588?

Answer: 12

Question 7

In how many different ways can 44100 be written as a product of 2 natural numbers?

Answer: 41

Question 8

In how many different ways can you write 294 as the sum of 2 or more consecutive natural numbers?

Answer: 5

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