How many integers between 250 and 300, inclusive, can be evenly divide

Question

How many integers between 250 and 300, inclusive, can be evenly divided by NEITHER 3 NOR 5?

A. 33

B. 28

C . 27

D. 25

E. 24

100mitra · Accepted Answer

Integers between 250 and 300 inclusive = (300 - 250) + 1 = 51

(1) Divisible 3 = (300-250)/3 + 1 = 17
(2) Divisible 5 = (300-250)/5 + 1 = 11
(3*5 = 15)
(3) Divisible 15 = (300-250)/15 + 1 = 4

Number of integers between 250 and 300, inclusive, evenly divided by NEITHER 3 NOR 5 
= 51 - (17 + 11 - 4) 
= 27

Option C

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poojapandav95 · Answer

Total integers between 250 and 300 = (300-250)+1 = 51

Total numbers divisible by 3: (last term divisible by 3 - first term divisible by 3)/3 + 1 = (300-252)/3 + 1 = 17
Total numbers divisible by 5: (last term divisible by 5 - first term divisible by 5)/5 + 1 = (300-250)/5 + 1 = 11
Total numbers divisible by 15: (last term divisible by 15 - first term divisible by 15)/15 + 1 = (300-255)/15 + 1 = 4

Number of integers divided by NEITHER 3 NOR 5 :

51-(17+11-4) = 27

Option C

lkshy · Answer

what is the significance of "evenly divided" in the question
I didnt understand that,

thanks

Faith09 · Answer

Hi ikshy

Evenly divided simply means divided without any remainder.
without any left over. hope that helps.

luigilosito · Answer

i don't understand why it is -4 and not +4

HarshavardhanR · Answer

Hey luigilosito,

We need to find the numbers between [250,300] that are not divisible by 3 or 5.
We have 17 numbers divisible by 3 and 11 numbers divisible by 5.
But some of these 17 numbers divisible by 3 are also part of the 11 numbers divisible by 5. For instance, 255 and 300 are both numbers that are divisible by 3 as well as 5. They will be part of both groups: the 17 numbers divisible by 3 as well as the 11 numbers divisible by 5.
There are 4 such numbers which are divisible by both 3 and 5.
So, when trying to count the numbers divisible by 3 or 5, if we simply add 17 and 11, we would be counting numbers those 4 numbers twice (255, 270, 285, and 300). Once because they are part of the 17 and once again because they are part of the 11. In reality, any number should only be counted once.
Thus, if we add 17 + 11, those 4 numbers get counted an extra time. To remove this redundancy, we simply need to subtract 4.
Thus, numbers from [250,300] that are divisible by 3 or by 5: 17 (div by 3) + 11 (div by 5) - 4 (to ensure that those 4 numbers are not getting double counted) = 24
Thus, numbers from [250,300] that are NOT divisible by 3 or by 5 = 51 - 24 = 27.

luigilosito

i don't understand why it is -4 and not +4

poojapandav95

Total integers between 250 and 300 = (300-250)+1 = 51

Total numbers divisible by 3: (last term divisible by 3 - first term divisible by 3)/3 + 1 = (300-252)/3 + 1 = 17
Total numbers divisible by 5: (last term divisible by 5 - first term divisible by 5)/5 + 1 = (300-250)/5 + 1 = 11
Total numbers divisible by 15: (last term divisible by 15 - first term divisible by 15)/15 + 1 = (300-255)/15 + 1 = 4

Number of integers divided by NEITHER 3 NOR 5 :

51-(17+11-4) = 27

Option C

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How many integers between 250 and 300, inclusive, can be evenly divide

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How many integers between 250 and 300, inclusive, can be evenly divide

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