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Question
In a Class of 120 students numbered 1 to 120, all even numbered students opt for Physics , those 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 subject ?
19
41
43
51
ANSWER : 2
Descrption
<pre> Physics takes = 120/2 = 60<br />Chemistry takes = 120/5 = 24<br />Mathematics takes = 120/7 = 17<br />Physics and chemistry = 120/10 = 12<br />Physics andmathematics = 120/14 = 8<br />Chemistry and mathematics = 120/35 = 3<br />Physics, Chemistry and mathematics = 120/70 = 1<br />So, Only physics and chemistry = 12 - 1 = 11<br />Only physics and mathematics = 8 - 1 = 7<br />Only Chemistry and mathematics = 3 - 1 = 2<br />Now, Only physics = 60 - 11 - 7 = 41<br />Only Chemistry = 24 - 11 - 2 - 1 = 10<br />Only mathematics = 17 - 7 - 2 - 1 = 7<br />Shortcut not taken none ofthe three = 120 - (41 + 10 + 7 + 11 + 7 + 2 + 1) = 12 - 79 = 41 </pre>
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