GMAT question - How many prime numbers are there which are greater t... - Review
Type: Problem Solving
Difficulty: 
How many prime numbers are there which are greater than 40 and less than 60?
- 4
- 5
- 6
- 7
- 8
Explanation
You are unlikely to have remembered the prime numbers up to 60 so we will have to do a bit of work to resolve this.
If we list all the numbers between greater than 40 and less than 60 then we can remove all the numbers which have factors other than themselves and one and this will leave us with the primes.
Start with all the numbers between 40 and 60
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59
The numbers ending in 0, 2, 4, 6 or 8 are divisible by 2 so we can strike out the numbers 42, 44, 46, 48, 50, 52, 54, 56 and 58 because they are not prime.
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59
And we can remove those with digits that sum to a multiple of 3 because they are divisible by 3. This enables us to strike out 45, 51 and 57.
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59
We do not need to check for numbers divisible by 4 because these will also be divisible by 2 and so we have already struck them out.
The numbers ending in 0 or 5 are divisible by 5 so we can strike out 55 because it is not prime.
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59
Similarly there is no need to check for divisibility by 6 because this has already been covered by 3 and 2.
Finally we need to check which are divisible by 7, there is no easy test for this but you should know your multiples of 7 well enough to see that 42, 49 and 56 are multiples of 7 which enables us to strike out 49.
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59
This leaves us with 5 prime numbers 41, 43, 47, 53 and 59, so B is the correct answer.
There is an error in your explaination.
"We do not need to check for numbers divisible by 4 because these will also be divisible by 3 and so we have already struck them out."
44, 52, 56 are number that are divisible by 4 and not 3. I think what you were trying to say was, we do not need to check for numbers divisible by 4 because they will also be divisible by 2.
Thanks for pointing out this typo, it has now been fixed