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how many prime numbers between 1 and 100

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how many prime numbers between 1 and 100

by money9111 » Mon Feb 01, 2010 8:22 pm
How many prime numbers between 1 and 100 are factors of 7,150?

a. one
b. two
c. three
d. four
e. five

I didn't even know how to start with this one... i've quickly established that prime numbers, consecutive integers, and divisibility are where I need to focus my attention - post prep class

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by kabirmohammed » Mon Feb 01, 2010 9:03 pm
the prime factors of 7150 are: 2, 5,5 13,11
total number of prime factors = 4
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by money9111 » Mon Feb 01, 2010 10:26 pm
hhmm see with this one i broke down the prime factors... but the "between 1 and 100" is what threw me off
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by diegow77 » Tue Feb 02, 2010 12:11 am
how do you go about solving this one quickly?
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by ajith » Tue Feb 02, 2010 1:00 am
diegow77 wrote:how do you go about solving this one quickly?
a. factorize the given number to prime factors
b. count the distinct no of prime numbers
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by sanju09 » Tue Feb 02, 2010 1:33 am
ajith wrote:
b. count the distinct no of prime numbers, like 2, 5,5 13,11.
right approach, though

2//7150
5//3575
5//715
11//143
13//13

that's it! 7150 = 2*5*5*11*13 with only [spoiler]four[/spoiler] distinct prime factors as 2, 5, 11, and 13.
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by amirp » Tue Feb 02, 2010 11:37 am
Faster way to factor this is to think first devide by 10 which is very easy then later break it down to 2 * 5

7150 / 10 = 715
715 / 5 = 143
143 / 11 = 13 ( if you want to know a number is divisible by 11, add the 1st and last numbers, if it equals the middle number, its divisible by 11 )

so you have

10 * 5 * 11 * 13
2 * 5 * 5 * 11 * 13

4 prime factors.
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by money9111 » Tue Feb 02, 2010 11:05 pm
I redid this problem today, and it was a cinch! I know you're thinking... "well I hope it was easy because of this post" but I had forgotten about this post, and when I saw the question again (after my class tonight) i was thinking to myself "oh there's only one way to solve this" - the correct way of course... it was nice to feel that way for once haah
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by boysangur » Fri Sep 03, 2010 8:38 pm
Just encountered this now. I knew how to approach it but what confuses me is that the problem doesn't ask for DISTINCT prime numbers. It just asks "how many prime numbers". So I answered five but apparently, the answer is four? What tells you guys it's asking for distinct numbers?
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by Gurpinder » Fri Sep 03, 2010 8:56 pm
money9111 wrote:How many prime numbers between 1 and 100 are factors of 7,150?

a. one
b. two
c. three
d. four
e. five

I didn't even know how to start with this one... i've quickly established that prime numbers, consecutive integers, and divisibility are where I need to focus my attention - post prep class

OA D
start by breaking down 7150 to its prime tree
750 = 11*13*5*5*2

and THATS IT!! we have our answer. there are 4 distinct prime factors of 7150.

(D) - four

wasn't that simple?!?!?! :D
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by sanju09 » Fri Sep 03, 2010 9:00 pm
boysangur wrote:Just encountered this now. I knew how to approach it but what confuses me is that the problem doesn't ask for DISTINCT prime numbers. It just asks "how many prime numbers". So I answered five but apparently, the answer is four? What tells you guys it's asking for distinct numbers?

The many prime numbers between 1 and 100, which are factors of 7,150, are the prime numbered factors of 7,150 only. We don't require the luxurious info that those primes are distinct too.

How many primes are there between 20 and 30?

We would count 23, 29 and would readily answer it's 2. Did they ask "How many DISTINCT primes are there between 20 and 30?"?
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by boysangur » Fri Sep 03, 2010 9:16 pm
sanju09 wrote:
boysangur wrote:Just encountered this now. I knew how to approach it but what confuses me is that the problem doesn't ask for DISTINCT prime numbers. It just asks "how many prime numbers". So I answered five but apparently, the answer is four? What tells you guys it's asking for distinct numbers?

The many prime numbers between 1 and 100, which are factors of 7,150, are the prime numbered factors of 7,150 only. We don't require the luxurious info that those primes are distinct too.

How many primes are there between 20 and 30?

We would count 23, 29 and would readily answer it's 2. Did they ask "How many DISTINCT primes are there between 20 and 30?"?
But let's say they asked "how many prime factors are there in 20?" We get 5*2*2. That's 3 prime factors that make up 20, but 2 of them are distinct factors. Or if they asked "how many prime factors make up 8?" wouldn't you answer 3, since it's 2*2*2?
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by sanju09 » Fri Sep 03, 2010 9:29 pm
boysangur wrote:
sanju09 wrote:
boysangur wrote:Just encountered this now. I knew how to approach it but what confuses me is that the problem doesn't ask for DISTINCT prime numbers. It just asks "how many prime numbers". So I answered five but apparently, the answer is four? What tells you guys it's asking for distinct numbers?

The many prime numbers between 1 and 100, which are factors of 7,150, are the prime numbered factors of 7,150 only. We don't require the luxurious info that those primes are distinct too.

How many primes are there between 20 and 30?

We would count 23, 29 and would readily answer it's 2. Did they ask "How many DISTINCT primes are there between 20 and 30?"?
But let's say they asked "how many prime factors are there in 20?" We get 5*2*2. That's 3 prime factors that make up 20, but 2 of them are distinct factors. Or if they asked "how many prime factors make up 8?" wouldn't you answer 3, since it's 2*2*2?
There is only one prime factor that makes 8 up, and that is 2. The three appearances of 2 are not for answering your question in bold above, these three appearances of 2 are rather helpful in answering

"How many factors are there for 8?"

Since, we have 8 = 2^3, so the answer would be 3 + 1 = 4.
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by Fractal » Mon Sep 19, 2011 4:31 am
boysangur wrote:Just encountered this now. I knew how to approach it but what confuses me is that the problem doesn't ask for DISTINCT prime numbers. It just asks "how many prime numbers". So I answered five but apparently, the answer is four? What tells you guys it's asking for distinct numbers?
I agree. I am also confused because the question doesn't say "different prime factors".

According to Manhattan GMAT, one can ask for

- different prime factors
- total prime factors (length)

So I had no idea whether to choose 4 or 5, because for me it is not clearly stated, what is really asked!
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