Latest Elitmus Aptitude Question SOLUTION: How many numbers from 0 to 351 are not divisible by 2,3,5 & 7 .

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(#M40033743) ELITMUS Numerical Ability question Keep an EYE

How many numbers from 0 to 351 are not divisible by 2,3,5 & 7 .

Asked In Elitmus sanjana (10 years ago)

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AVIJIT  (10 years ago)

there is only one number inbetween 0 to 351 which is divisble by 2,3,5&7 is 210.
there is only 352 numbers are present inbetween 0 to 351.
so 351 are not divisible by 2,3,5 & 7;
ans is 351

Is this solution Helpfull? Yes (26) | No (11)  

wilson paul  (10 years ago)

from o to 100 number of number divisible by 2=50
similarly frm 100 to 200 =50
from 200 to 300 =50
from 300 to 351 we have 25
from 0 t0 100 number of numbers divisble by 3 but not 2 is 17
similarly frm 100 to 200 =17
frm 200 to 300 =17
frm 300 to 351=8
from 0 to 100 the number of nubers divisible by 5 bt not 2 and 3 is 7
similarly frm 100 to 200 =7
frm 200 to 300 =7
frm 300 to 351 we have only 1
frm 0 to 100 the no of numbers divisible by 7 bt not 2,3,5 are =4
similarly from 100 to 200= 4
frm 200 to 300 =4
frm 300 to 350 we have 0
hence totally....frm 0 to 351 the number of numbers not divisible by 2,3,5,7 are
352-(50+50+50+25+17+17+17+8+7+7+7+1+4+4+4+0)
352-(274)
ans=78

Is this solution Helpfull? Yes (19) | No (1)  

Shireesh Mehta  (10 years ago)

LCM of 2,3,5 and 7 is 210.
The next number divisible by all 4 numbers will be a multiple of 210.
The nearest multiple of 210 will be 210*2=420 which is greater than 351.
So, only 2 numbers are divisible i.e. 0 and 210.

Is this solution Helpfull? Yes (11) | No (3)  

hp maity  (10 years ago)

i think guys u are taking it wrong it was actually asking for the number which are not individually not divisible by 2,3,5,7, like 11,13,17,19,23, etc and their multiples .. am i ri8??

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aman kumar tiwari  (10 years ago)

0.........because lcm of 2,3,5&7 is 210 so no number are divisible between 0to 351

Is this solution Helpfull? Yes (2) | No (13)  

AMIT JAISWAL  (9 years ago)

divisibility by 2 for no.s b/w 0 to 351-
no b/w 0 to 300=150 and no b/w 300 to 351=25
total=175

divisibility by 3 but not 2 for no.s b/w 0 to 351-
series of such no.s = 3,9, 15,.........., 351
by A>P. total no of terms => 351=3+(n-1)6
so, n =59

divisibility by 5 but not 2&3 for no.s b/w 0 to 351-

no.s divisible by 5 but not 2&3 between 0 to 100 = 7
similarly count between 100 to 300 = 14 more such terms
now no.s between 300 to 351 divisible by 5 but not 2&3 = 305,325,335=3
total no of terms = 7+14+3=24

divisibility by 7 but not 2,3&7 for no.s b/w 0 to 351-
from 0 to 100 (7,49,77,91)=4
similarly from 100 to 200 (119,133,161,182)=4
similarly from 200 to 300 (203,217,259,287)=4
from 300 to 351 (301,329,343)=3

total no of terms = 4+4+4+3=15

so numbers divisible b/w 0 to 351 not divisible by 2,3,5&7 = 352-(175+59+24+15)
= 79 answer

Is this solution Helpfull? Yes (2) | No   

CHAITANYA  (10 years ago)

All prime numbers between 0-351 are not divisible by 2,3,5,7.

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

shubhrant tripathi  (10 years ago)

Ans. 2
0 and 210

Is this solution Helpfull? Yes | No (4)  

amit kumar  (8 years ago)

total number is 88
nos divisible by 2 = 180
nos divisible by 3 (not by 2)= 59
nos divisible by 5(not by 2 3) = 12
nos divisible by 7 ( not by 2,3,5) = 13

summing up we get 264 which are divisible
so nos not divisible is 352-264 = 88

as the total numbers are 352

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