edited by
2,035 views
3 votes
3 votes

Consider the set of integers $\{1,2,3,\ldots,5000\}.$ The number of integers that is divisible by neither $3$ nor $4$ is $:$

  1. $1668$
  2. $2084$
  3. $2500$
  4. $2916$
edited by

1 Answer

Best answer
9 votes
9 votes

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

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 by
Answer:

Related questions

3 votes
3 votes
1 answer
1
admin asked May 13, 2019
1,259 views
Given the following four functions $f_{1}(n)=n^{100},$ $f_{2}(n)=(1.2)^{n},$ $f_{3}(n)=2^{n/2},$ $f_{4}(n)=3^{n/3}$ which function will have the largest value for suffi...
4 votes
4 votes
2 answers
2
1 votes
1 votes
2 answers
3
5 votes
5 votes
2 answers
4
admin asked May 13, 2019
1,050 views
Given the sequence $A,B,B,C,C,C,D,D,D,D,\ldots$ etc$.,$ that is one $A,$ two $B’s,$ three $C’s,$ four $D’s,$ five $E’s$ and so on, the $240^{th}$ latter in the se...