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If k is a positive integer, how many unique prime factors does 14k

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If k is a positive integer, how many unique prime factors does 14k [#permalink]

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If k is a positive integer, how many unique prime factors does 14k have ?

(1) k^4 is divisible by 100
(2) 50*k has 2 prime factors

Give me an algebraic solution. And i will tell you where you went wrong :twisted:
[Reveal] Spoiler: OA

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Originally posted by stonecold on 22 Nov 2016, 11:24.
Last edited by hazelnut on 12 May 2017, 00:31, edited 3 times in total.
Renamed the topic and edited the question.
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Re: If k is a positive integer, how many unique prime factors does 14k [#permalink]

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New post 22 Nov 2016, 13:20
It depends on whether you're referring to prime factors or unique prime factors. I assume from the wording of statement 2 that it's the latter, but on the GMAT they'd have to be more specific.
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Re: If k is a positive integer, how many unique prime factors does 14k [#permalink]

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New post 22 Nov 2016, 13:23
ccooley wrote:
It depends on whether you're referring to prime factors or unique prime factors. I assume from the wording of statement 2 that it's the latter, but on the GMAT they'd have to be more specific.



Thank you.
I have edited the Post.
P.S => Its good to finally see someone from mgmat on this forum.
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Re: If k is a positive integer, how many unique prime factors does 14k [#permalink]

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New post 22 Nov 2016, 17:25
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1) k has to be a multiple of 2 and 5. 14 carries the primes 2 and 7 so three primes

2. if 50 K only has two primes we can look what primes 50 can be broken down into
2 and 5 and 14 has 2 and 7 so again three primes
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Re: If k is a positive integer, how many unique prime factors does 14k [#permalink]

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New post 22 Nov 2016, 20:57
joannaecohen wrote:
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1) k has to be a multiple of 2 and 5. 14 carries the primes 2 and 7 so three primes

2. if 50 K only has two primes we can look what primes 50 can be broken down into
2 and 5 and 14 has 2 and 7 so again three primes


OA is C :)
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Re: If k is a positive integer, how many unique prime factors does 14k [#permalink]

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stonecold wrote:
if k is a positive Integer,how many unique Prime Factors Does 14k have ?

(1) k^4 is divisible by 100
(2)50*k has 2 Prime Factors

Give me an algebraic solution. And i will tell you where you went wrong :twisted:



(1) \(k^4\) is divisible by \(100=10^2\), we have \(k^4=10^2 k'\).

Since the left side is a double square of \(k\) and the right side contains only a square of 10, we must have \(k'=10^2 \times k"^4\).
So \(k^4=10^4 \times k"^4 \implies k=10k"\) or \(k\) is divisible by 10.

This means that \(k\) has at least 2 prime factors 2 and 5, so \(14k=2 \times 7 \times k\) has at least 3 prime factors 2, 5, and 7.

However, we cannot know the extract number of prime factors that \(14k\) has. Insufficient.

(2) \(50k=2 \times 5^2 \times k\). Since \(50=2 \times 5^2\) has 2 prime factors 2 and 5 and \(50k\) has only 2 prime factors, it is deduced that \(k\) has at most 2 prime factors 2 and 5.

If \(k\) has only one prime factors 2, \(14k\) has 2 prime factors 2 and 7.
If \(k\) has two one prime factors 2 and 5, \(14k\) has 3 prime factors 2, 5 and 7.
Insufficient.

Combine (1) & (2):
(1): \(k\) has at least 2 prime factors 2 and 5
(2): \(k\) has at most 2 prime factors 2 and 5

(1)+(2): \(k\) does have 2 prime factors 2 and 5.
So \(14k\) has 3 prime factors 2, 5, and 7. Sufficient.

The answer is C

ccooley wrote:
It depends on whether you're referring to prime factors or unique prime factors. I assume from the wording of statement 2 that it's the latter, but on the GMAT they'd have to be more specific.

Please correct me, but I see no diffirence in these two sentences:
(1) 14k has 3 prime factors.
(2) 14k has 3 unique prime factors.
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Re: If k is a positive integer, how many unique prime factors does 14k [#permalink]

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New post 22 Nov 2016, 23:11
Bunnuel can you pls explain the answer

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Re: If k is a positive integer, how many unique prime factors does 14k [#permalink]

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New post 22 Nov 2016, 23:39
nguyendinhtuong wrote:
stonecold wrote:
if k is a positive Integer,how many unique Prime Factors Does 14k have ?

(1) k^4 is divisible by 100
(2)50*k has 2 Prime Factors

Give me an algebraic solution. And i will tell you where you went wrong :twisted:



(1) \(k^4\) is divisible by \(100=10^2\), we have \(k^4=10^2 k'\).

Since the left side is a double square of \(k\) and the right side contains only a square of 10, we must have \(k'=10^2 \times k"^4\).
So \(k^4=10^4 \times k"^4 \implies k=10k"\) or \(k\) is divisible by 10.

This means that \(k\) has at least 2 prime factors 2 and 5, so \(14k=2 \times 7 \times k\) has at least 3 prime factors 2, 5, and 7.

However, we cannot know the extract number of prime factors that \(14k\) has. Insufficient.

(2) \(50k=2 \times 5^2 \times k\). Since \(50=2 \times 5^2\) has 2 prime factors 2 and 5 and \(50k\) has only 2 prime factors, it is deduced that \(k\) has at most 2 prime factors 2 and 5.

If \(k\) has only one prime factors 2, \(14k\) has 2 prime factors 2 and 7.
If \(k\) has two one prime factors 2 and 5, \(14k\) has 3 prime factors 2, 5 and 7.
Insufficient.

Combine (1) & (2):
(1): \(k\) has at least 2 prime factors 2 and 5
(2): \(k\) has at most 2 prime factors 2 and 5

(1)+(2): \(k\) does have 2 prime factors 2 and 5.
So \(14k\) has 3 prime factors 2, 5, and 7. Sufficient.

The answer is C

ccooley wrote:
It depends on whether you're referring to prime factors or unique prime factors. I assume from the wording of statement 2 that it's the latter, but on the GMAT they'd have to be more specific.

Please correct me, but I see no diffirence in these two sentences:
(1) 14k has 3 prime factors.
(2) 14k has 3 unique prime factors.


Hi
I think i can answer that.
In mgmat books the explanation is given as follows =>
n=2*3^2 => two unique prime factors and 3 Total prime factors.
They refer to total Prime factors as "length" where we just have to add the exponents.
It just Creates confusion if you ask me since in GMAT/general mathematics we always write prime factors as to unique prime factors.

Regards
Stone Cold
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Re: If k is a positive integer, how many unique prime factors does 14k [#permalink]

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stonecold wrote:
nguyendinhtuong wrote:
ccooley wrote:
It depends on whether you're referring to prime factors or unique prime factors. I assume from the wording of statement 2 that it's the latter, but on the GMAT they'd have to be more specific.

Please correct me, but I see no diffirence in these two sentences:
(1) 14k has 3 prime factors.
(2) 14k has 3 unique prime factors.


Hi
I think i can answer that.
In mgmat books the explanation is given as follows =>
n=2*3^2 => two unique prime factors and 3 Total prime factors.
They refer to total Prime factors as "length" where we just have to add the exponent.
It just Creates confusion if you ask me since in GMAT/general mathematics we always wrote prime factors as to unique prime factors.

Regards
Stone Cold


Still confused :-D As I see, \(n=2*3^2\) still has only 2 prime factors 2 and 3.

Oh, I got this. In MGMAT, they stated that: 72 splits into 5 total prime factors: 2x3x2x2x3. However, 72 still does only 2 prime factors 2 and 3.

Hence, your question meets no confusion between "prime factors" and "unique prime factors".
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Re: If k is a positive integer, how many unique prime factors does 14k [#permalink]

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New post 16 Dec 2017, 12:49
stonecold wrote:
If k is a positive integer, how many unique prime factors does 14k have ?

(1) k^4 is divisible by 100
(2) 50*k has 2 prime factors

Give me an algebraic solution. And i will tell you where you went wrong :twisted:


Bunuel can you help us out? lol
Re: If k is a positive integer, how many unique prime factors does 14k   [#permalink] 16 Dec 2017, 12:49
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