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Re: How many positive integers less than 100 are neither multiples of 2 or [#permalink]
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22 Feb 2017, 12:11
there are 50 odd nos less than 100 which are not multiples of 2. within these 50 numbers we simply need to remove 50 odd multiples of 3 i.e 3, 9 ,15.......,99. This is an AP series with a=3 d=6 & Tn = 99 Therefore no of odd multiples of 3 less than 100 are: 99 = 3+(n1)6 = 17 So numbers neither multiple of 2 nor 3 are = 5017 = 33



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Re: How many positive integers less than 100 are neither multiples of 2 or [#permalink]
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27 Mar 2017, 06:07
I have an intuitive way of seeing it that seems right..
1,2,3. 2 and 3 are multiples of 2 and 3
4,5,6. 4 and 6 are multiples of 2 and 3.
7,8,9. 8 and 9 are multiples of 2 and 3.
I didn't extrapolate but it seems to be a pattern here. 1/3 of such a series will not be multiples  Hence 99/3 = 33. Does it make sense?



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Re: How many positive integers less than 100 are neither multiples of 2 or [#permalink]
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29 Mar 2017, 10:00
devbond wrote: How many positive integers less than 100 are neither multiples of 2 or 3.
a)30 b)31 c)32 d)33 e)34 \ We can use the following equation: Number of integers from 1 to 99 inclusive = number of integers that are multiples of 2 or 3 + number of integers that are neither multiples of 2 nor 3 Furthermore: Number of integers that are multiples of 2 or 3 = number of multiples of 2 + number of multiples of 3  number of multiples of 2 and 3 Notice that the number of multiples of 2 and 3 is also the number of multiples of 6. Let’s determine the number of multiples of 2 from 1 to 99 inclusive using the following equation: (largest multiple of 2 in the set  smallest multiple of 2 in the set)/2 + 1 (98  2)/2 + 1 = 49 Now we can determine the number of multiples of 3 from 1 to 99 inclusive using the same concept: (99  3)/3 + 1 = 33 Finally, let’s determine the number of multiples of 6, since some multiples of 2 are also multiples of 3; we must subtract those out so they are not doublecounted. (96  6)/6 + 1 = 16 Thus, there are 49 + 33  16 = 66 multiples of 2 or 3 from 1 to 99, inclusive. Therefore, there are 99  66 = 33 multiples from 1 to 99 inclusive that are not multiples of 2 or 3. Answer: D
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Re: How many positive integers less than 100 are neither multiples of 2 or [#permalink]
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15 Apr 2017, 12:44
devbond wrote: How many positive integers less than 100 are neither multiples of 2 or 3.
a)30 b)31 c)32 d)33 e)34 Set comprises the integers 199 inclusive. Number of items in set=99. Number of integers that are a multiple of 2: [(982)/2)]+1=49 Number of integers that are a multiple of 3: [(993)/2)]+1=33. Of these, 16 are even and are therefore counted in the number of multiples of 20 (49). So there are 17 additional integers to add that are multiples of 3 but not multiples of 2. 99(49+17)=9966=33 Agree?



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Re: How many positive integers less than 100 are neither multiples of 2 or [#permalink]
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18 Apr 2017, 06:49
how i approached this problem  we have to eliminate all the multiples of 2 & 3... Therefore, within 100 it's all about the prime numbers and 1.
There are 25 prime numbers 
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Out of which 2 & 3 are not included so  23. Also, there is 1. So 24.
Next the multiples of the prime numbers  5*5, 5*7, 5*11, 5*13, 5*17, 5*19, 7*7, 7*11, 7*13
So altogether there are 33 such numbers.
(Note: It may take a bit long but it's another method to think about.)



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Re: How many positive integers less than 100 are neither multiples of 2 or [#permalink]
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30 Aug 2017, 17:00
Last numer less than 100 divisible by 2 is 98 Then 98/2 = 49....You need to add 1 to count number 98..so 49+1=50
Last number less than 100 divisible by 3 is 99 Then 99/3= 33.... You need to add 1 to count number 99..so 33+1=34
We need to fin multiples of 6 Last number less than 100 divisible by 6 is 96 Then 96/6= 16.... You need to add 1 to count number 96..so 16+1=17...
Remove duplicity with Venn diagrams A+B AB ....50+3417= 67 numbers. 10067 = 33
Hence D!



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Re: How many positive integers less than 100 are neither multiples of 2 or [#permalink]
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28 Oct 2017, 01:18
devbond wrote: How many positive integers less than 100 are neither multiples of 2 or 3.
a)30 b)31 c)32 d)33 e)34 Neither a multiple of 2 or 3 = Total numbers in the set  Multiples of 2 and 3. Multiples of 2 and 3 = Total Multiples of 2 and 3 (including the common multiples)  Common multiples of 2 and 3. Total Multiples of 2 and 3 (including the common multiples): 1) Multiples of 2 from 2 to 98 = 98/2 = 49 2) Multiples of 3 from 3 to 99 = 99/3 = 33 49+33=82. Common multiples of 2 and 3: LCM of 2 and 3 = 6 Multiples of 6 from 6 to 96 = 96/6 = 16 Thus, multiples of 2 and 3 = 8216 = 66 Neither a multiple of 2 or 3 = 9966 = 33 D



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Re: How many positive integers less than 100 are neither multiples of 2 or [#permalink]
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05 Dec 2017, 04:53
devbond wrote: How many positive integers less than 100 are neither multiples of 2 or 3.
a)30 b)31 c)32 d)33 e)34 My take on solving this one quickly and efficiently, The question is simply asking about the NUMBER of positive integers LESS THAN 100 that are neither multiples of 2 or 3. Firstly, calculating the number of positive integers LESS THAN 100 that are multiples of 2 = {[(Last multiple of 2 which is less than 100)  (First multiple of 2 which greater than or equal to 1)] / 2} + 1 = [(98  2)/2] + 1 = 48 + 1 = 49
Secondly, calculating the number of positive integers LESS THAN 100 that are multiples of 3 = {[(Last multiple of 3 which is less than 100)  (First multiple of 3 which greater than or equal to 1)] / 3} + 1 = [(99  3)/3] + 1 = 32 + 1 = 33
Thirdly, calculating the number of positive integers LESS THAN 100 that are multiples of 6 NOW YOU MAY ASK WHAT IS THE NEED FOR CALCULATING THE NUMBER OF +ve INTEGERS LESS THAN 100 THAT ARE MULTIPLES OF 6 > Because 2 AND 3 have some common multiples which are counted TWICE. Therefore, to delete those numbers from the count, we need to do so. = {[(Last multiple of 6 which is less than 100)  (First multiple of 6 which greater than or equal to 1)] / 6} + 1 = [(96  6)/6] + 1 = 15 + 1 = 16
ANS : 99  49 33 + 16 = 33 option D




Re: How many positive integers less than 100 are neither multiples of 2 or
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