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Lakshman Patel RJIT
asked
in Quantitative Aptitude
May 13, 2019
edited
May 14, 2019
by Lakshman Patel RJIT

1,162 views
7 votes

Best answer

$S = \{1,2,3,\ldots,4999,5000\}$

Let '**A**' be the set of integers divisible by $3 \implies A =\{3,6,9,12,15,\ldots,4998\}$

Let '**B**' be the set of integers divisible by $4 \implies B= \{4,8,12,16,\ldots,5000\}$

Let '**C**' be the set of integers divisible by both $3$ and $4 \implies C = \{12,24,36,\ldots,4992\}$

$|A| = 3+(n-1)3 = 4998 \implies n = 4998/3 = 1666$

$|B| = 4+(n-1)4 = 5000 \implies n = 5000/4 = 1250$

$|C| =12+(n-1)12 = 4992 \implies n = 4992/12 = 416$

Divisible by $3$ or $4:$ $\{3,4,6,8\dots 5000\}$ : $|D| = |A| + |B| -|C|$

$= 1666+1250-416$

$= 2500$

Number of integers that is divisible by neither $3$ nor $4$

$= |S| - |D|$

$= 5000-2500$

$= 2500$

So, C is the correct answer.

edited
Aug 9, 2020
by subbus

$\textbf{the set of integers that are divisible by 3 can be represented by the general term 3n.}$

$\text{For n=1,2,3......we get the set as {3,6,9,......}}$

$\text{for finding the number of the elements in the set}$

$3n\leq 5000 \Rightarrow n\leq \frac{5000}{3}= 1666.66$

$\therefore{the ~last~ n~ would ~be~1666~which ~is~the~count}$

$\text{For n=1,2,3......we get the set as {3,6,9,......}}$

$\text{for finding the number of the elements in the set}$

$3n\leq 5000 \Rightarrow n\leq \frac{5000}{3}= 1666.66$

$\therefore{the ~last~ n~ would ~be~1666~which ~is~the~count}$

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@ankitgupta.1729, I used this method to get the closest multiple of $12$ less than $5000$.

So, $\frac{5000}{12}=416.6667$ Then I subtracted $416$ from this answer, then multiplied it by $12$ . Here I got $8$.

So, subtracted $8$ from $5000$ to get $4992$ which is the last multiple of 12 less than $5000$.

I want to know if I can do this in similar other problems?

So, $\frac{5000}{12}=416.6667$ Then I subtracted $416$ from this answer, then multiplied it by $12$ . Here I got $8$.

So, subtracted $8$ from $5000$ to get $4992$ which is the last multiple of 12 less than $5000$.

I want to know if I can do this in similar other problems?

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