Latest TCS Aptitude Question SOLUTION: 20. How many numbers are there from 100 to 1200 which are not divisible either by 2, 3, or 5?

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20. How many numbers are there from 100 to 1200 which are not divisible either by 2, 3, or 5?

Asked In TCS Bishal Pandey (10 years ago)

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Sumit Bhattacharyya  (10 years ago)

tn=a+(n-1)d
For 2=>n=551
For 3=>n=367
For 5=>n=221
For (2*3)=6=>n=184
For (3*5)=15=>n=74
For (5*2)=10=>n=111
For LCM (2,3,5)=30=>n=37
So NUMBERS are=(551+367+221)-(184+74+111)+37
=1139-369+37
=807

Therefore no of numbers not divisible=1200-99-807=294

Is this solution Helpfull? Yes (54) | No (4)  

pratik jitendra malviya  (10 years ago)

Sn=a+(n-1)d
For 2=>n=550
For 3=>n=267
For 5=>n=220
But in 5 Half of the terms will end with 0 hence they are also divisible by 2
So 1098-(550+367+110)=1098-1027=71

Is this solution Helpfull? Yes (1) | No (8)  

Debu Singh  (10 years ago)

tn=a+(n-1)d
For 2=>n=551
For 3=>n=367
For 5=>n=221
For (2*3)=6=>n=184
For (3*5)=15=>n=74
For (5*2)=10=>n=111
For LCM (2,3,5)=30=>n=37
So NUMBERS are=(551+367+221)-(184+74+111)+37
=1139-369+37
=807

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

Pradeep   (10 years ago)

1/2 of the no.s divisible by 2 so 550 no.s divisible and for5 as already cancelled the
10 20 30 40........by 2 so in every 10no.s one will be divisible for 55 tens. 55 can divisible
So 550-55=495
Then after removing 2 and 5 multiples in every 30 no.s 4 will divisible
For 495 no.s 16*4+2=66
So ans is 495-66=429

Is this solution Helpfull? Yes (1) | No   

Pradeep   (10 years ago)

294 answer

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Priyanka Shekhaw3at  (10 years ago)

what is 1098 here

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Vivek Banga  (10 years ago)

Priyanka..1098 is the total no. of terms from a=100 and tn=1200..

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mritunjay kumar  (10 years ago)

ans--1139...

Is this solution Helpfull? Yes | No (2)  

anand singh  (10 years ago)

n(AUBUC) = n(A) + n(B) + n(C) - n(A intersectn B) - n(B intersectn C) - n(A intersectn C) + n(A intersectn B intersectn C)

n(2U3U5) = n(2) + n(3) + n(5) - n(6) - n(15) - n(10) + n(30)

--> n(2U3U5) = 600 + 400 + 240 - 200 - 80 - 120 + 40 = 880

Hence number of numbers not divisible by any of the numbers 2, 3, and 5

= 1100 - 880 = 220.

Is this solution Helpfull? Yes | No (4)  

Mudassir Fazal  (10 years ago)

total number of terms b/w 100 and 1200 are 1001
out of it 501 are even
remaining terms=500
numbers divisible by 3
3*34=102
3*400=1200
so numbers divisible by 3 are 400-34+1=367
remaining terms=500-367=133
similarly number divisible by 5 221
remainig number 133-221= -88
now adding multiples of 2*3(6),2*5(10),3*5(15) as they are reapetely subtracted
ie
we get 281 as total number not divisible by 2, 3,or 5

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Somobrata Ghosh  (7 years ago)

why - 99 from 1200??

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