TIFR CSE 2013 | Part A | Question: 12

Question

Among numbers $1$ to $1000$ how many are divisible by $3$ or $7$?

• A. $333$
• B. $142$
• C. $475$
• D. $428$
• E. None of the above

Answer 1

Divisible by $3$ $=$ $\dfrac{1000}{3} = 333$

Divisible by $7$ $=$ $\dfrac{1000}{7}= 142 $

Divisible by both $=\dfrac{1000}{\text{LCM OF 3 & 7}} = \dfrac{1000}{21} = 47 $

$n(A\cup B) = n(A) +n(B) - n(A\cap B)$
$\qquad\qquad\;= 333 + 142 - 47 =  428.$

Correct Answer: $D$

Comments

\text{} is quite handy in tex :)

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but not for Pragy Agrawal.he is good editor. 

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Good to see more people using latex- will be handy in IISc./IITs :)

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Just a small correction. Here we are not talking about probabilities nor power set. We are instead talking about the cardinalities of sets.

So appropriate notation would be:

$n(A\cup B) = n(A) + n(B) - n(A \cap B)$