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Question
How many integers are there from 500 to 2000 that leave a remainder of 2 on division by 5 and a remainder of 1 on division by 3?
How many integers are there from 500 to 2000 that leave a remainder of 2 on division by 5 and a remainder of 1 on division by 3?
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Solution
The correct option is A 100
The number should be of the form 5a+2 and 3b+1.
The LCM of 5 and 3 is 15.
A number of form 5a+2 can be written as 15c+2 (or) 15c+7 (or) 15c+12.
A number of form 3b+1 can be written as 15d+1 (or) 15d+4 (or) 15d+7.
The common term is 15c+7.
The numbers in the form of 15c+7 are 7, 22, 37, 52, ..…..502, 517, ……1987.
502 = 15(33)+7
517 = 15(34)+7
……………
1987 = 15(132)+7
There are 100 numbers in this sequence
100
The number should be of the form 5a+2 and 3b+1.
The LCM of 5 and 3 is 15.
A number of form 5a+2 can be written as 15c+2 (or) 15c+7 (or) 15c+12.
A number of form 3b+1 can be written as 15d+1 (or) 15d+4 (or) 15d+7.
The common term is 15c+7.
The numbers in the form of 15c+7 are 7, 22, 37, 52, ..…..502, 517, ……1987.
502 = 15(33)+7
517 = 15(34)+7
……………
1987 = 15(132)+7
There are 100 numbers in this sequence
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