In this case, it means unique.

But shouldn't the answer be (D)?

Aren't both statements suggesting that R is a multiple of S?

Gurpinder wrote:In this case, it means unique.

But shouldn't the answer be (D)?

Aren't both statements suggesting that R is a multiple of S?

Hi Gurpinder,

My answer was also D, but when I checked it was A. The source of this problem is question 7, GMATPrep, Practice Content, Review Questions, Data Sufficiency.

Any suggestions?

Thanks!

stmt1,

every factor of s is also a factor of r.

-->r=s*a[ where a is an integer]

r/s=s*a/s=a

Suff

stmt2,

Every prime factor of s is also a prime factor of r

r/s is an integer[100/10].r and s can be expressed with 2 and 5.

r/s is not an integer[10/100].r and s can be expressed with 2 and 5.

Insuff

Pick A

Hey guys,

Great question, and great work on statement 1. I've always found the words-and-not-equations problems to be a little tricky (your mind wants to see "math", but you're seeing more verbal-style logic), but manageable if you take the time to flush out the statements and even use examples to help yourself get the point of what the statement is saying.

Statement 1:

EVERY factor of s is also a factor of r

This means that whatever you can divide into s, you can also divide into r. If s is divisible by 2, 3, and 6, then r is also divisible by 2, 3 and 6. You can't, therefore, put anything into the denominator that wouldn't cancel with the numerator...whatever is in s will automatically be in r (which may or may not have extra factors), so there's no choice but to say that r is divisible by s.


Statement 2:

EVERY PRIME factor of s is also a prime factor of r

Here, the difference is that we're only talking about prime factors. Say that s has the prime factors 2 and 3...that means that r will also have prime factors 2 and 3. But that's all we know about r - we can guarantee that it's a multiple of 6 in that case, but s could have as many 2s and 3s as we want to give it and we'd still only be able to know that r is divisible by 2 and 3. Say that s is 36 - its prime factorization is 2*2*3*3...but we only know that x has the same "prime factors", not the same "prime factors and number of prime factors". Because statement 2 allows for both r/s = 6/6 and r/s = 6/36, it's not sufficient.


For really any DS problems, but especially those that give written rules that may seem mathematically nebulous because you don't quite have an equation/inequality, I like to test each statement by trying to stretch the rule as far as it will go. If you come up with a hypothetical that isn't specifically prohibited by the rule (like that 6/36 above), it's allowable.

Thank you Selango & Brian for your feedback.

Statement (2) still is unclear for me.

(2) Every prime factor of s is also a prime factor of r

Could we rephrase: each prime number (factor) of s should be at least once in r? Or each prime factor of s could refer to the same prime factor of r?

For example: r=2*3 and s=2*2*3 (the 2 two's refer to the same 2 of r)

lavinia wrote:Thank you Selango & Brian for your feedback.

Statement (2) still is unclear for me.

(2) Every prime factor of s is also a prime factor of r

Could we rephrase: each prime number (factor) of s should be at least once in r? Or each prime factor of s could refer to the same prime factor of r?

For example: r=2*3 and s=2*2*3 (the 2 two's refer to the same 2 of r)

Further explanation:

Stmnt 2 does not say that r and s has exact same nubmer of prime factors but the same prime factors. So in case s has more prime or normal factors than r the result r/s will not be an integer.

Thanks Gig92 for your explanation. Now it makes sense.

gig92 wrote:

lavinia wrote:Thank you Selango & Brian for your feedback.

Statement (2) still is unclear for me.

(2) Every prime factor of s is also a prime factor of r

Could we rephrase: each prime number (factor) of s should be at least once in r? Or each prime factor of s could refer to the same prime factor of r?

For example: r=2*3 and s=2*2*3 (the 2 two's refer to the same 2 of r)

Further explanation:

Stmnt 2 does not say that r and s has exact same nubmer of prime factors but the same prime factors. So in case s has more prime or normal factors than r the result r/s will not be an integer.

lavinia wrote:If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r
(2) Every prime factor of s is also a prime factor of r

[spoiler]Answer: A[/spoiler]

"Every prime factor" means unique prime factors of s or each prime factor of s?

Thanks!

Whats the source of this question?

Gurpinder wrote:

lavinia wrote:If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r
(2) Every prime factor of s is also a prime factor of r

[spoiler]Answer: A[/spoiler]

"Every prime factor" means unique prime factors of s or each prime factor of s?

Thanks!

Whats the source of this question?

The source of this question is GMATPrep/ Practice Content/ Review Questions/ Data Sufficiency/ Question 7.

lavinia wrote:

Gurpinder wrote:

lavinia wrote:If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r
(2) Every prime factor of s is also a prime factor of r

[spoiler]Answer: A[/spoiler]

"Every prime factor" means unique prime factors of s or each prime factor of s?

Thanks!

Whats the source of this question?

The source of this question is GMATPrep/ Practice Content/ Review Questions/ Data Sufficiency/ Question 7.

That's interesting. I saw the EXACT SAME question on grockit.com

I've never used crockit website before, but it looks interesting. Any feedback?

Gurpinder wrote:

lavinia wrote:

Gurpinder wrote:

lavinia wrote:If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r
(2) Every prime factor of s is also a prime factor of r

[spoiler]Answer: A[/spoiler]

"Every prime factor" means unique prime factors of s or each prime factor of s?

Thanks!

Whats the source of this question?

The source of this question is GMATPrep/ Practice Content/ Review Questions/ Data Sufficiency/ Question 7.

That's interesting. I saw the EXACT SAME question on grockit.com

lavinia wrote:I've never used crockit website before, but it looks interesting. Any feedback?

Gurpinder wrote:

lavinia wrote:

Gurpinder wrote:

lavinia wrote:If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r
(2) Every prime factor of s is also a prime factor of r

[spoiler]Answer: A[/spoiler]

"Every prime factor" means unique prime factors of s or each prime factor of s?

Thanks!

Whats the source of this question?

The source of this question is GMATPrep/ Practice Content/ Review Questions/ Data Sufficiency/ Question 7.

That's interesting. I saw the EXACT SAME question on grockit.com

I just bought their premium membership. I think its awesome. You can practice a specific area with specific difficulty level. What more an you ask for. And you get detailed explanations.