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# How many even number in the range between 10 to 100 inclusive are not

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How many even number in the range between 10 to 100 inclusive are not  [#permalink]

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21 Aug 2016, 08:48
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Difficulty:

75% (hard)

Question Stats:

56% (02:02) correct 44% (02:09) wrong based on 230 sessions

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How many even number in the range between 10 to 100 inclusive are not divisible by 3

A) 15
B) 30
C) 31
D) 33
E) 46

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Re: How many even number in the range between 10 to 100 inclusive are not  [#permalink]

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21 Aug 2016, 09:04
2
NandishSS wrote:
How many even number in the range between 10 to 100 inclusive are not divisible by 3

A)15
B)30
C)31
D)33
E)46

We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)

For 2,

10,12,14...100

using AP formula, we can say 100 = 10 + (n-1) *2

or n=46.

For 6,

12,18,...96

using AP formula, we can say 96 = 12 + (n-1) *6

or n=15.

Hence, only divisible by 2 but not 3 = 46-15 = 31. hence, Answer C
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Re: How many even number in the range between 10 to 100 inclusive are not  [#permalink]

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23 Aug 2016, 06:04
1
I would be using the set theory here =>
Number of terms divisible by 2=> 46
Number of terms divisible by 3=> 30
Number of terms divisible by 6=>15
Hence A intersection B =15
Only A= A-A intersection B=> 46-15=> 31

SMASH that C
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Re: How many even number in the range between 10 to 100 inclusive are not  [#permalink]

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01 May 2017, 01:36
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Total Number of even numbers in 10-100 inclusive = 46 = 50(total in 100) - 4 (2,4,6,8).

Total numbers divisible by 3 in range 10-100 =$$\frac{99 - 12}{3}+ 1$$ = $$\frac{87}{3} +1$$ = 30 of which half will be even numbers. = 15.

Total even numbers not divisible by 3 are = 46 - 15 = 31.
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Re: How many even number in the range between 10 to 100 inclusive are not  [#permalink]

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01 May 2017, 09:51
First, let's consider the number of even numbers between 10 and 100, (extremes included)

(100-10)/2 + 1 = 46 even numbers

Now of these 46 even numbers, there are numbers which are also multiples of 3. The question asks us to find how many of these 46 numbers are not multiples of 3.

Remember, for an even number to be multiple of 3 , it has to be a multiple of 6 as well.

so, we've to weed out the multiples of 6 out of the above 46 numbers,

(96-12)/6 + 1 = 15 multiples of 6.

so the remaining numbers = 46 - 15 = 31 (C)
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Re: How many even number in the range between 10 to 100 inclusive are not  [#permalink]

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06 May 2017, 16:14
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NandishSS wrote:
How many even number in the range between 10 to 100 inclusive are not divisible by 3

A) 15
B) 30
C) 31
D) 33
E) 46

We can first determine the number of even numbers from 10 to 100 inclusive:

(100 - 10)/2 + 1 = 90/2 + 1 = 46

We know that if a number is even and it is also divisible by 3, then it’s divisible by 6. Therefore, we need to determine the number of multiples from 10 to 100 inclusive and exclude these multiples from the 46 even numbers we’ve determined.

The number of multiples of 6 from 10 to 100 inclusive is:

(96 - 12)/3 + 1 = 84/6 + 1 = 14 + 1 = 15

Since there are 46 even numbers and 15 multiples of 6 (which are divisible by 3) from 10 to 100 inclusive, there must be 46 - 15 = 31 even numbers that are not divisible by 3.

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Re: How many even number in the range between 10 to 100 inclusive are not  [#permalink]

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21 Aug 2018, 06:49
RMD007 wrote:
Total Number of even numbers in 10-100 inclusive = 46 = 50(total in 100) - 4 (2,4,6,8).

Total numbers divisible by 3 in range 10-100 =$$\frac{99 - 12}{3}+ 1$$ = $$\frac{87}{3} +1$$ = 30 of which half will be even numbers. = 15.

Total even numbers not divisible by 3 are = 46 - 15 = 31.

But why you did not include the 0 as an even number, the game changes, when we include 0 in the number list. Please explain.
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Re: How many even number in the range between 10 to 100 inclusive are not &nbs [#permalink] 21 Aug 2018, 06:49
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