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

Question

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

abhimahna · Accepted Answer

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

stonecold · Answer

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

RMD007 · Answer

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.

Aldorado · Answer

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)

ScottTargetTestPrep · Answer

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.

Answer: C

Seryozha · Answer

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.

DelademAnku · Answer

why 96-12? Can you explain a little further

WiziusCareers1 · Answer

The problem asks for the number of even integers in the range from 10 to 100 (inclusive) that are not divisible by 3.

We can solve this using the principle of inclusion-exclusion (or simply subtraction) by following these steps:

Step 1:  Find the total number of even numbers in the range  .

The even numbers are 10,12,14,...,100. This is an arithmetic progression. The number of terms can be found with the formula:

Count = {(Last Number−First Number)/Step} + 1 
Total Even Numbers = {(100 - 10)/2} + 1 = 46
There are 46 even numbers in the range.

Step 2:  Find the number of even numbers that are divisible by 3 in the range  .

A number that is both even (divisible by 2) and divisible by 3 must be divisible by the least common multiple of 2 and 3, which is 6. We need to find the number of multiples of 6 in the range  .

Let 6k be a multiple of 6. We are looking for integers k such that:
10 ≤ 6k ≤ 100
1.66 ≤ k ≤ 16.66
Since k must be an integer, the possible values for k are {2,3,4,...,16}.

The number of such multiples is:
Count=16−2+1=15
There are 15 even numbers (multiples of 6) that are divisible by 3 in the range.

Step 3:  Find the number of even numbers that are not divisible by 3.
Subtract the number of even numbers that are divisible by 3 (from Step 2) from the total number of even numbers (from Step 1).
Even Numbers Not Divisible by 3 = Total Even Numbers − Even Numbers Divisible by 3
Even Numbers Not Divisible by 3 = 46 − 15 = 31
The final count is 31, which is option C.

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

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