Latest Elitmus Aptitude Question SOLUTION: How many numbers less than 500 are divisible by 2 or 3 or 4 or 5 or 7 or 21?

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(#M40019957) ELITMUS General Ability question DIVISIBILITY Keep an EYE

How many numbers less than 500 are divisible by 2 or 3 or 4 or 5 or 7 or 21?

Asked In Elitmus Arpit Jaiswal (10 years ago)

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siddanth  (10 years ago)

no of prime no's below 500 is 95
excluding 2,3,5,7, it is 91
no's not divisible 2,3,4,5,7,21, are
11*(11,13,17,19,23,29,31,37,41,43) i.e 10
13*(13,17,19,23,29,31,37) i.e 7
17*(17,19,23,29) i.e 4
19*(19,23) i.e 2
initially 1 is also not divisible
total = 91+10+7+4+2+1= 115
answer 500-115 = 385

Is this solution Helpfull? Yes (19) | No (6)  

VIKAS SINGH  (10 years ago)

first we find the no.s which r not divisible by 2 r 3 r 4 r 5 r 7 r 21.
all these no.s will be prime no.s.
since within 100 there r 23 prime no.s which r not devisible by 22 r 3 r 4 r5 r 7 r21. same for 100-200. so total prime no. within 500 will be 115.
so no.s that r devisible by 2 r 3 r 4 r 5 r 7 r 21 will be 499-115=384.

Is this solution Helpfull? Yes (15) | No (19)  

Pradeep Rawat  (10 years ago)

@vikas singh : there are 97 prime numbers between 2-499.

so by excluding 2,3,5,7 there will be 93 numbers + 1 (i.e 1 is not divisible by any number). so total 92 numbers which will not divide by these numbers.

so 499-92 = 407.

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ranjeet singh chauhan  (10 years ago)

@siddanth : could u please explain ur solution....

Is this solution Helpfull? Yes (1) | No (4)  

mohit  (8 years ago)

div by 2-250
div by 3-166
div by 5-100
div by 7-71
total-587
/////no need to find 4, 21
div by 2&3-83
div by2&5-50
div by2&7-35
div by3&5-33
div by3&7-23
total-238
now
div by 2&3&5-16
div by2&3&7-111
div by3&5&7-4
div by2&5&7-7
total-38
and
div by 2&3&5&7- 2
So sol is 587-224+38-2=385

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