Prime Numbers

[GmatKiss]

How many prime numbers exist between 200 and 220?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

[neelgandham]

Answer - b)One - 211

Approach -

Step 1 - The list 200-220 has 11 even numbers and 10 odd numbers.

Step 2 - We are down to 10 possible-prime-numbers as the rest 11 are divisible by 2, hence non prime.

Step 3 - Out of the 10 possible-prime-numbers, 4 are divisible by 3 (201,207,213,219), hence non prime. so we are down to 6 possible-prime-numbers.

Step 4 - Out of the remaining 6 possible-prime-numbers, 2 are multiples of 5, hence non prime. Now, we are down to 4 possible-prime-numbers.

Step 5 - Now, the numbers 203, 209, 211, 217 are leftover. As the upper limit (200-220) is 220 and the nearest square is 225(15^2), check if the remaining 4 possible-prime-numbers are divisible by at least one among the prime numbers below 15(2,3,5,7,11,13,17,19).

203 and 217 are divisible by 7

209 is divisible by 11

So 211 is the only one remaining !

Looks and feels lengthy, but is really easy.(a 1 minute problem)