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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?


  1. 101

  2. 102

  3. 103

  4. 100


Solution

The correct option is D

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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