In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects? Choose the correct choice from the following options: A) 19 B) 41 C) 21 D) 26 E) 25
Number of students who took at least one of the three subjects can be found by finding out A U B U C, where A is the set of those who took Physics, B the set of those who took Chemistry and C the set of those who opted for Math.   Now, AUBUC = A + B + C - (A n B + B n C + C n A) + (A n B n C)   A is the set of those who opted for Physics = 120/2= 
<gadget id="calculator">120/2</gadget>
<output>60</output>
60 students   B is the set of those who opted for Chemistry= 120/5= 
<gadget id="calculator">120/5</gadget>
<output>24</output>
24   C is the set of those who opted for Math= 120/7 = 17.   The 10th, 20th, 30th…… numbered students would have opted for both Physics and Chemistry.   Therefore, A n B = 120/10= 
<gadget id="calculator">120/10</gadget>
<output>12</output>
12   The 14th, 28th, 42nd…. Numbered students would have opted for Physics and Math.   Therefore, C n A= 120/14 = 8   The 35th, 70th …. Numbered students would have opted for Chemistry and Math.   Therefore, A n B = 120/35 = 3   And the 70th numbered student would have opted for all three subjects.   Therefore, AUBUC = 60 + 24 + 17 - (12 + 8 + 3) + 1= 
<gadget id="calculator">60 + 24 + 17 - (12 + 8 + 3) + 1</gadget>
<output>79</output>
79.   Number of students who opted for none of the three subjects= 120 - 79= 
<gadget id="calculator">120 - 79</gadget>
<output>41</output>
41.   ANSWER:41
<result>B</result>
In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?