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Q #11
⏰ :

Directions: Read the following information to answer the question.

A number N (N < 500) when divided by 12, 14 and 18 gives a remainder of 11 in each case. What will be the remainder when N is divided by 11?

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Answer: 10 Explanation: LCM of 12,14 and 18 is 252 So 252+11=263 When 263 is divided by 11 it leaves remainder 10. Hence proved.

Q #12
⏰ :

Directions: Read the following information to answer the question.

What is the highest number that will divide 68 and 84 leaving a remainder of 3 and 6, respectively?

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Answer:13 Explanation:68-3=65 84-6=78 Hcf of 65 and 78 is 13. Hence proved.

Q #13
⏰ :

Directions: Read the following information to answer the question.

What is the highest number that will divide 87 and 122, leaving a remainder of 3 in each case?

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Answer:7 Explanation: 87-3=84 122-3=119. Hcf of 84 and 119 is 7. Hence proved.

Q #14
⏰ :

Directions: Read the following information to answer the question.

What is the highest number N that will divide 49, 73 and 105, leaving the same remainder in each case?

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Answer:8 Explanation: let us say that the no ‘d’ divides 49,73 and 105 to leave remainder ‘r’ So 49-r,73-r,105-r are divisible by d. (73-r)-(49-r) and (105-r)-(73-r) are divisible by ‘d’. 24 and 56 are divisible by’d’. HCF of 24 and 56 is 8. Hence proved.

Q #15
⏰ :

Directions: Read the following information to answer the question.

Summish wants to pack 108 oranges, 180 apples and 240 pears in boxes. His friend Arun lays down a condition that a box should have only one kind of fruit and the number of fruits in all boxes should be the same and number of boxes should also be minimum. How many boxes will Summish need to pack all the fruits?

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Answer:44 Explanation: HCF of 108,180,240 is 12. Now for oranges required boxes =108/12=9 Similarly for apple=180/12=15 For pears 240/12=20 Total boxes required 9+15+20=44 Hence proved.