x is a positive integer less than 100. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
Choose the correct choice from the following choices.
A) 14
B) 22
C) 23
D) 24
E) 25
the nubmer which when divided by 7 leaves remainder 1 should be of the form 7k+1   this number when divided by 3 leaves remainder 2.   so,   (7k+1)-2 should be divisible by 3 or 7k-1 should be divisible by 3.   we now put the values of k starting from 0 to find first number divisible by 3   we find 1st number at k= 1   thus smallest number will be 7(1)+1 = 8   now,   next number will be = 8+ lcm of 37   i.e 29   now we will find number of all such values less than 500 by using the formula for last term of an a.p   8+(n-1)21=100   n=14.42   or n= 14   14nswer:- 14
<result>A</result>
x is a positive integer less than 100. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?