Latest Athenahealth Aptitude Question SOLUTION: How many integers between 50 and 100 can be evenly divided by neither 3 nor 5?

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How many integers between 50 and 100 can be evenly divided by neither 3 nor 5?

Asked In Athenahealth vishnuvardhan (10 years ago)

Unsolved Read Solution (17)

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Read Solution (17) :

Rajkumar R.S  (10 years ago)

divisible by 3 between 50 and 100 = 17 (51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99)

divisible by 5 between 50 and 100 = 9 (55,60,65,70,75,80,85,90,95)

Common divisible for 5 and 3 = 3 (60, 75, 90)

Total divisible by 5 and 3 between 50 and 100 = 17+9-3 => 23

There are 49 numbers between 50 to 100 i.e 51 to 99

so the integers that are not divisible by 3 and 5 => 49 - 23 => 26

Is this solution Helpfull? Yes (28) | No   

Revathy  (10 years ago)

divisible by 3 between 50 and 100 = 16 (51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,99)

divisible by 5 between 50 and 100 = 11 (50,55,60,65,70,75,80,85,90,95,100)

Common divisible for 5 and 3 = 3 (60, 75, 90)

So, total divisible by 5 and 3 between 50 and 100 = 16+11-3 => 24

Therefore the integers that are not divisible by 3 and 5 = 51 - 24 => 27

Is this solution Helpfull? Yes (3) | No (13)  

allu jyothi  (10 years ago)

24

Is this solution Helpfull? Yes (2) | No (1)  

Clair Christ D  (10 years ago)

26
count of numbers divided by 3 : 17
count of numbers divided by 5 : 11
count of numbers divided by both 3 and 5 : 3
so totally 17 + 11 - 3 = 25
51 - 25 = 26

Is this solution Helpfull? Yes (2) | No (1)  

krishna babu Bellamkonda  (10 years ago)

total 18 integers
51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99

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

Bhuvana  (10 years ago)

total divisible by 5 and 3 between 50 and 100 = 16+11-3 => 24
not divisible = 49 - 24= 25

Is this solution Helpfull? Yes (1) | No   

kavya  (9 years ago)

divisible by 3 between 50 and 100 = 17 (51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99)

divisible by 5 between 50 and 100 = 9 (55,60,65,70,75,80,85,90,95)

Common divisible for 5 and 3 = 3 (60, 75, 90)

Total divisible by 5 and 3 between 50 and 100 = 17+9-3 => 23

There are 49 numbers between 50 to 100 i.e 51 to 99

so the integers that are not divisible by 3 and 5 => 49 - 23 => 26

Is this solution Helpfull? Yes (1) | No   

Muneeswaran  (9 years ago)

divide/3 numbers are={51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99}=count(17)
divide/5 numbers are={55,60,65,70,75,80,85,90,95,}=count(9)
common numbers are={60,75,90}=count(3)
left out the common numbers= total((17+9)-3)
=26-3
total numbers are starts from 51 to 99 is 49
=49-23
answer=26

Is this solution Helpfull? Yes (1) | No   

Lakshman  (10 years ago)

24
total-no.of divisible
(51-27)=24 (divisible by 3=17,divisible by 5=10)

Is this solution Helpfull? Yes | No (1)  

Rajkumar R.S  (10 years ago)

divisible by 3 between 50 and 100 = 16 (51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,99)

divisible by 5 between 50 and 100 = 9 (55,60,65,70,75,80,85,90,95)

Common divisible for 5 and 3 = 3 (60, 75, 90)

Total divisible by 5 and 3 between 50 and 100 = 16+9-3 => 22

There are 49 numbers between 50 to 100 i.e 51 to 99

so the integers that are not divisible by 3 and 5 => 49 - 22 => 27

Is this solution Helpfull? Yes | No (3)  

Gowrim  (9 years ago)

answer = 15

numbers between 50 and 100 = 49

numbers not divisible by 3 or 5 = 49 - 23 = 26

since evenly divided, number of prime numbers between 50 and 100 = 11

so, 26 - 11 = 15

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Gowrim  (9 years ago)

answer = 15

numbers between 50 and 100 = 49

numbers not divisible by 3 or 5 = 49 - 23 = 26

since evenly divided, number of prime numbers between 50 and 100 = 11

so, 26 - 11 = 15

Is this solution Helpfull? Yes | No (1)  

sravani  (9 years ago)

26 intergers
52,53,56,58,59
61,62,64,67,68,
71,73,74,76,77,79,
82,83,86,88,89,
91,92,94,97,98

Is this solution Helpfull? Yes | No   

Manoj Prabhakar R  (8 years ago)

divisible by 3 between 50 and 100 = 17 (51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96,99)

divisible by 5 between 50 and 100 = 9 (55,60,65,70,75,80,85,90,95)

Common divisible for 5 and 3 = 3 (60, 75, 90)

Total divisible by 5 and 3 between 50 and 100 = 17+9-3 => 23

There are 49 numbers between 50 to 100 i.e 51 to 99

so the integers that are not divisible by 3 and 5 => 49 - 23 => 26

Is this solution Helpfull? Yes | No   

sunilvignesh.v.j  (8 years ago)

divisible by 3 and 5 are 51,54,55,57,60,63,65,66,69,70,72,75,78,80,81,84,85,87,90,93,95,96,99...totally 23 numbers are divisible by 3 and 5....so,48(between 50 and 100 ,so 50&100 neglected) - 23 ==== 25 numbers can be evenly divided by neither 3 nor 5

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keerthana chennamsetty  (8 years ago)

23 integers will not be neither divided by 3 or 5.

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Kannan Mohan  (8 years ago)

ANS : 26
17 numbers divisible by 3 from 50 to 100
11 numbers divisible by 5 from 50 to 100
So 26 numbers in total
51-26=25 integers

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