If N is the sum of four different primes each greater than 200, what i

Question

If N is the sum of four different primes each greater than 200, what is the least possible value of N?

A. 887
B. 890
C. 899
D. 903
E. 921

BrentGMATPrepNow · Accepted Answer

APPROACH #1 : Identify the 4 smallest prime greater than 200 
This will require a lot of work, but when we're done we get: 211, 223, 227 and 229
So, the sum = 211 + 223 + 227 + 229 = 890
Answer: B

APPROACH #2 : Recognize that ALL prime numbers greater than 2 are ODD 
So, the sum = ODD + ODD + ODD + ODD = EVEN
Answer: B

Paras96 · Answer

Because all the prime number greater than 2 are odd,

ODD + ODD + ODD + ODD = EVEN

Among the options, only B is even.

Therefore,  answer is B

dhruva09 · Answer

BrentGMATPrepNow   Bunuel , Is there any quick way of identifying/ reaching to a prime number.

Bunuel · Answer

Generally, there’s no simple way to check if a very large number is prime (unless it has small factors, which are easier to check). For numbers like that, you’d need a computer to test.

On the GMAT, you won’t encounter a large number to factorize unless there’s a clear shortcut.

Here is a way though:

•  Verifying the primality  (checking whether the number is a prime) of a given number  n  can be done by trial division, that is to say dividing  n  by all integer numbers smaller than  \sqrt{n} , thereby checking whether  n  is a multiple of  m\leq{\sqrt{n}} .

Example:  Verifying the primality of  161 :  \sqrt{161}  is little less than  13 , from integers from  2  to  13 ,  161  is divisible by  7 , hence  161  is not prime.

Note that, it is only necessary to try dividing by  prime  numbers up to  \sqrt{n} , since if  n  has any divisors at all (besides 1 and  n ), then it must have a prime divisor.

Having said that, in this question we don't need to find the actual primes. The sum of four odd primes (since all are greater than 2) must be even, and the only even option is B.

dhruva09 · Answer

Thanks for the prompt response  Bunuel . As usual, this is helpful.

If N is the sum of four different primes each greater than 200, what i

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If N is the sum of four different primes each greater than 200, what i

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