Scroll:Heuristics >> Common Factor Method >> ps (529)


Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.



 

1)  

The number of cookies in a container can be put into packets of 4, 11 or 8 with no leftover.

What is the least possible number of cookies in the container


Answer:_______________




2)  

At a fun fair, 3 toy cars - A, B, and C are made to move round a circular track. Toy Car A passes the starting line once every 4 seconds, while Toy Car B passes the starting line once every 7 seconds and Toy Car C passes the starting line once every 8 seconds. If the 3 toy cars pass the starting line at the same time now, how many seconds later will the 3 toy cars next cross the starting line together again

seconds


Answer:_______________




3)  

A red light bulb flashes once every 7 seconds, while a blue light bulb flashes once every 4 seconds and a green light bulb flashes once every 8 seconds. If the 3 light bulbs flash at the same time now, how many seconds later will they next flash together again

seconds


Answer:_______________




4)  

A signboard was decorated with flashing bulbs of 3 colours. The blue bulbs flashed every 4 minutes. The red bulbs flashed every 7 minutes. The orange bulbs flashed every 8 minutes. If they flash together at the same time now, how many minutes later would they flash together again

minutes


Answer:_______________




5)  

Ovini, Kumutha and Tamilselvi visit the library regularly.
Ovini visits the library every 4 days.
Kumutha visits every 5 days while Tamilselvi visits every 8 days.
If they met each other today, how many days later will they meet again


Answer:_______________




6)  

Traffic Light A flashes once every 2 seconds, while Traffic Light B flashes once every 5 seconds and Traffic Light C flashes once every 4 seconds. If the 3 traffic lights flash at the same time now, how many seconds later will they next flash together again

seconds


Answer:_______________




7)  

Jeevini and Mithra are jogging in a park. Jeevini takes 4 minutes to jog round the park once, while Mithra takes 5 minutes. If they both set off at the same time from the same point, how many minutes later will they meet each other again

minutes


Answer:_______________




8)  

The number of cookies in a container can be put into packets of 2, 9 or 4 with no leftover.

What is the least possible number of cookies in the container


Answer:_______________




9)  

At a fun fair, 3 toy cars - A, B, and C are made to move round a circular track. Toy Car A passes the starting line once every 4 seconds, while Toy Car B passes the starting line once every 11 seconds and Toy Car C passes the starting line once every 8 seconds. If the 3 toy cars pass the starting line at the same time now, how many seconds later will the 3 toy cars next cross the starting line together again

seconds


Answer:_______________




10)  

A red light bulb flashes once every 5 seconds, while a blue light bulb flashes once every 4 seconds and a green light bulb flashes once every 8 seconds. If the 3 light bulbs flash at the same time now, how many seconds later will they next flash together again

seconds


Answer:_______________




 

1)  

The number of cookies in a container can be put into packets of 4, 11 or 8 with no leftover.

What is the least possible number of cookies in the container

Answer: 88


SOLUTION 1 :

Step 1: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, ...
Step 2: Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, ...
Step 3: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, ..

The least possible number of cookies in the container is 88.



2)  

At a fun fair, 3 toy cars - A, B, and C are made to move round a circular track. Toy Car A passes the starting line once every 4 seconds, while Toy Car B passes the starting line once every 7 seconds and Toy Car C passes the starting line once every 8 seconds. If the 3 toy cars pass the starting line at the same time now, how many seconds later will the 3 toy cars next cross the starting line together again

Answer: 56 seconds


SOLUTION 1 :

Step 1: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, ...
Step 2: Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, ...
Step 3: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, ..

The 3 toy cars will cross the starting line together again 56 seconds later.

 



3)  

A red light bulb flashes once every 7 seconds, while a blue light bulb flashes once every 4 seconds and a green light bulb flashes once every 8 seconds. If the 3 light bulbs flash at the same time now, how many seconds later will they next flash together again

Answer: 56 seconds


SOLUTION 1 :

Step 1: Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, ...
Step 2: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...
Step 3: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, ..

They will flash together again 56 seconds later.



4)  

A signboard was decorated with flashing bulbs of 3 colours. The blue bulbs flashed every 4 minutes. The red bulbs flashed every 7 minutes. The orange bulbs flashed every 8 minutes. If they flash together at the same time now, how many minutes later would they flash together again

Answer: 56 minutes


SOLUTION 1 :

Step 1: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, ...
Step 2: Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, ...
Step 3: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, ..

They will flash together again 56 minutes later.



5)  

Ovini, Kumutha and Tamilselvi visit the library regularly.
Ovini visits the library every 4 days.
Kumutha visits every 5 days while Tamilselvi visits every 8 days.
If they met each other today, how many days later will they meet again
Answer: 40


SOLUTION 1 :

Step 1: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, ...
Step 2: Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
Step 3: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, ..

They will meet again 40 days later.



6)  

Traffic Light A flashes once every 2 seconds, while Traffic Light B flashes once every 5 seconds and Traffic Light C flashes once every 4 seconds. If the 3 traffic lights flash at the same time now, how many seconds later will they next flash together again

Answer: 20 seconds


SOLUTION 1 :

Step 1: Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, ...
Step 2: Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60,65, 70, 75, 80, 85 ...
Step 3: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, ..

They will flash together again 20 seconds later.



7)  

Jeevini and Mithra are jogging in a park. Jeevini takes 4 minutes to jog round the park once, while Mithra takes 5 minutes. If they both set off at the same time from the same point, how many minutes later will they meet each other again

Answer: 20 minutes


SOLUTION 1 :

Step 1: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, ...
Step 2: Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...

They will meet again 20 minutes later.



8)  

The number of cookies in a container can be put into packets of 2, 9 or 4 with no leftover.

What is the least possible number of cookies in the container

Answer: 36


SOLUTION 1 :

Step 1: Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, ...
Step 2: Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, ...
Step 3: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, ..

The least possible number of cookies in the container is 36.



9)  

At a fun fair, 3 toy cars - A, B, and C are made to move round a circular track. Toy Car A passes the starting line once every 4 seconds, while Toy Car B passes the starting line once every 11 seconds and Toy Car C passes the starting line once every 8 seconds. If the 3 toy cars pass the starting line at the same time now, how many seconds later will the 3 toy cars next cross the starting line together again

Answer: 88 seconds


SOLUTION 1 :

Step 1: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, ...
Step 2: Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, ...
Step 3: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, ..

The 3 toy cars will cross the starting line together again 88 seconds later.

 



10)  

A red light bulb flashes once every 5 seconds, while a blue light bulb flashes once every 4 seconds and a green light bulb flashes once every 8 seconds. If the 3 light bulbs flash at the same time now, how many seconds later will they next flash together again

Answer: 40 seconds


SOLUTION 1 :

Step 1: Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, ...
Step 2: Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...
Step 3: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, ..

They will flash together again 40 seconds later.