Problem Solving

francoisph wrote:Hi,

please any ideas?

The sum of prime numbers that are greater than 60 but less than 70 is?


A 67
B 128
C 191
D 197
E 260


thks

Solution:

A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.

Let's list the numbers from 61 to 69.

61, 62, 63, 64, 65, 66, 67, 68, 69

Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.

We are now left with: 61, 63, 65, 67, 69

We can next eliminate 65 because 65 is a multiple of 5.

We are now left with 61, 63, 67, 69.

To eliminate any remaining values, we would look at those that are multiples of 3. If you don't know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.

We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.

Thus, we can eliminate 63 and 69 from the list because they are not prime.

Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum of 61 and 67 is 128.

The answer is B

Here is a useful rule: If a two-digit number is a prime, it can't be divisible by any of the single-digit primes. That is, it can't be divisible by 2, 3, 5 and 7. In other words, if you have a two-digit number that is not divisible by 2, 3, 5 and 7, it must be a prime. If you have trouble seeing that 61 and 67 are prime, I would suggest that you review your multiplication tables. Doing so will allow you to quickly see that 61 and 67 are not multiples of a given single-digit number, such as 7.

Hi All,

Most of the posts in this thread are over 3 years old, so I imagine that the original posters are probably not on the site any more.

To address the point brought up by singalong - GMAT questions are not designed to force you to think about large groups of numbers one at a time, so you're not going to see a question that asks for "the sum of all the primes from 50 to 5,000." You will see questions about sets of numbers, sequences, Number Properties, etc., but those questions are almost always built around a pattern of some kind. In those cases, the goal is to find the pattern, not do a series of never-ending calculations.

Here, the task was relatively straight-forward: consider 9 numbers, find the ones that are prime and add them up. You'll find that the "math" involved in most Quant questions is just as straight-forward as the math in this question (and not that 'crazy').

GMAT assassins aren't born, they're made,
Rich