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
how many prime numbers between 1 and 100
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- money9111
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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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- ajith
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a. factorize the given number to prime factorsdiegow77 wrote:how do you go about solving this one quickly?
b. count the distinct no of prime numbers
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ajith wrote:
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.
right approach, thoughb. count the distinct no of prime numbers, like 2, 5,5 13,11.
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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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.
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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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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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?
- Gurpinder
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start by breaking down 7150 to its prime treemoney9111 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
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?!?!?!
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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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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?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?"?
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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 answeringboysangur wrote: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?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?"?
"How many factors are there for 8?"
Since, we have 8 = 2^3, so the answer would be 3 + 1 = 4.
The mind is everything. What you think you become. -Lord Buddha
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I agree. I am also confused because the question doesn't say "different prime factors".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?
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!