Problem Solving

The question is properly worded.
You're asked for the number of different primes. So, if we say that there are five different primes (2, 5, 5, 11, 13), then we're incorrectly stating that 5 and 5 are different primes, when they are not.

Cheers,
Brent

Sorry, I just re-read the original question and realized that the word "different" does not appear - my bad. That said, the answer is still the same.

If you're asked to find the number of "things" you can only count each thing once.
For example, if Al, Bob and Cam are in a room and we're asked to determine how many people are in the room, we can't answer 4: Al, Bob, Cam and Cam.
So, even if the question doesn't include the word "different," it is implied that we can't count the same number twice.

Cheers,
Brent

jenlee wrote:This question confuses me. It is from the OG 12th Ed, pg 175 #159

How many prime numbers between 1 and 100 are
factors of 7,150 ?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five

It is a pretty simple question, but it asks for how many prime numbers, so I said 5 (2, 5, 5, 11, 13) and not how many DIFFERENT prime numbers (2, 5, 11, 13) which is the correct answer. Is this bad wording or should I assume next time I see a similar question that they are asking for the number of different prime numbers? Or is it something with the factors that I am missing?

Solution:

We start by prime factoring 7,150.

7,150 = 715 x 10 = 143 x 5 x 10

At this point we must be careful. Don't incorrectly conclude that 143 is prime. Using our divisibility rules, we can determine that 143 is divisible by 11. A number is divisible by 11 if the sum of the odd-numbered place digits minus the sum of the even-numbered place digits is divisible by 11. We can test 143 to prove this:

1 + 3 - 4 = 4 - 4 = 0

Since zero is divisible by 11, we know that 143 is divisible by 11. We can now finish the prime factorization.

143 x 5 x 10 = 11 x 13 x 5 x 5 x 2

11 x 13 x 5^2 x 2

Thus we can see that there are 4 different prime factors of 7,150.

Answer: D

Hi All,

We're asked for the number of prime numbers between 1 and 100 that are factors of 7,150. Based on the Answers, there will be at least one - but no more than five - prime numbers, so a bit of 'brute force' Arithmetic is really all that's needed to answer this question.

To start, since 7150 is a multiple of 10, you should recognize two primes immediately: 2 and 5 (since 2x5 = 10)

7150 =
(715)(10) =
(715)(2)(5)

Next, we have to break down the 715; since it ends in a '5', we know that we can divide out that 5...
(715)(2)(5) =
(5)(143)(2)(5)

The question at this point is whether '143' is a prime number of not. Thankfully, there's not much potential work to do; since 12^2 = 144, we know that we only have to check up to 11. So will 7 or 11 divide evenly into 143?

You might recognize that 7 would divide evenly into 140... and then 147... but it celery doesn't divide evenly into 143. So what about 11? Yes, 11 DOES divide evenly into 143... 13 times. Thus, we have...
(5)(143)(2)(5) =
(5)(11)(13)(2)(5)

Thus, we have a total of 4 prime numbers.

Final Answer: D

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