How many ODD integers n, where 100 <= n <= 200, are divisible neither by seven nor by nine?  Choose the correct choice from the following:  A) 37  B) 38  C) 39  D) 40  E) 46
Total Integers from 100 to 200 inclusive = 101 (51 even and 50 odd)   Total Odd Integers from 100 to 200 = 50   Total No. that are multiple of 7 from 1-200 = 200/7 = 28 (i.e. 14 even and 14 odd)   Total No. that are multiple of 7 from 1-100 = 100/7 = 14 (i.e. 7 even and 7 odd)   Total No. that are ODD multiple of 7 from 100-200 = 14-7= 
<gadget id="calculator">14-7</gadget>
<output>7</output>
7   Total No. that are multiple of 9 from 1-200= 200/9 = 22 (i.e. 11 even and 11 odd)   Total No. that are multiple of 9 from 1-100 = 100/9 = 11 (i.e. 5 even and 6 odd)   Total No. that are ODD multiple of 9 from 100-200 = 11-6= 
<gadget id="calculator">11-6</gadget>
<output>5</output>
5   Total No. that are odd multiple of 7 and 9 will be multiple of 63 and count of such numbers from 100-200= 1   So Total No. that are odd multiple of 7 and/or 9 from 100-200 = 7+5-1= 
<gadget id="calculator">7+5-1</gadget>
<output>11</output>
11   So Total No. that are NOT odd multiple of 7 and/or 9 from 100-200= 50-11= 
<gadget id="calculator">50-11</gadget>
<output>39</output>
39   Answer: Option 39
<result>C</result>
How many ODD integers n, where 100 <= n <= 200, are divisible neither by seven nor by nine?