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Q #6
:

Directions: Read the following information to answer the question.

What is the Least 3 digit number that is exactly divisible by 4, 7 and 8?

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Answer : 112 Solution: LCM of 4,7,8 is 56 The smallest 3 digit no. that can be divided by 4,7,8 will also be divided by 56. (56*2=112)----3 digit no. So 112 is the smallest 3 digit no. i.e. closest to 100 and of 3 digits. Hence proved

Q #7
:

Directions: Read the following information to answer the question.

How many two digit numbers are there, which when divided by 3, 6 and 8 will leave a remainder of 2 ?

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Answer:4 Explanation: LCM of 3,6and 8 is 24. 24*1+2=26 24*2+2=50 24*3+2=74 24*4+2=98 So there are 4 numbers of two digits. Hence proved.

Q #8
:

Directions: Read the following information to answer the question.

What is the least number which when divided by 3, 6, and 8 will leave remainders of 1, 4, and 6 respectively?

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Answer :22 Explanation: Here 3-1=2,6-4=2,8-6=2 The required no.= LCM of (3,6,8)-2=24-2=22 So 22 is the number.

Q #9
:

Directions: Read the following information to answer the question.

How many 3 digit numbers are there which when divided by 5,7 and 15 will give a remainder of 4?

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Answer :9 Explanation: LCM of 5,7 and 15 is 105 Therefore add 4 to LCM =105+4=109 So 109 is the first desired three digit no. Three digits numbers which upon division by 5,7 and 15,give remainder of 4 are 109,214,319,424,529,634,739,844. So 9 is the correct option. Hence proved.

Q #10
:

Directions: Read the following information to answer the question.

Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had?

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Answer :23 Solution : books are between 15 and 30 if he gives to two of his friends then no. of books may be 17,19,21,23,25,27,29.again he give books to of his 3 friends then no. of books may be 17,23 and 29. Now he have to give books to of bhis 4 friends then no. of books will be 23. Hence proved.