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
OA:C
A)15
B)30
C)31
D)33
E)46
OA:C
Hi NandishSS,
When dealing with a question that involves a long sequence of numbers, there is almost always a pattern involved. If you don't immediately 'see' the pattern though, you can still figure it out by doing a little bit of 'brute force' work. Here's how you can do that work here:
We're told to focus on the EVEN numbers from 10 to 100, inclusive. We're asked how many of those numbers are NOT divisible by 3...
Let's start at the beginning and work our way up:
10 - NOT divisible
12 - Divisible
14 - NOT divisible
16 - NOT divisible
18 - Divisible
20 - NOT divisible
22 - NOT divisible
24 - Divisible
....
96 - Divisible
98 - NOT divisible
100 - NOT divisible
Notice that, starting at 12, every THIRD number is divisible by 3. That means we can break this sequence down into 'sets of 3' with an extra number 'left over' (the 10). In the sets of 3, 2/3 of the numbers are NOT divisible by 3.
We can calculate the total numbers of terms as (100 - 10)/2 + 1 = 46 terms
This tells us that there are 15 sets of 3 terms, and 2/3 of those terms are NOT divisible by 3. Thus, there are 30 terms that are NOT divisible by 3. When we include the 10, there are now 30+1 = 31 terms.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
