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If r and s are positive integers, is r/s an integer? [#permalink]
 23 Feb 2012, 08:13
Question Stats:
55% (01:37) correct
44% (00:35) wrong based on 21 sessions
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.
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Re: If r and s are positive integers, is r/s an integer? [#permalink]
23 Feb 2012, 08:26
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is x/y is an integer [#permalink]
11 Apr 2012, 13:05
All
could you provide ur thoughts on this please?
if x and y are positive integers, is x/y is an integer?
(1) every prime factor of x is also the prime factor of y
(2) every factor of x is also a factor of y
i went with D, since the word "every" confused me
but seems missed something
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Re: is x/y is an integer [#permalink]
11 Apr 2012, 13:11
Galiya wrote: All
could you provide ur thoughts on this please?
if x and y are positive integers, is x/y is an integer?
(1) every prime factor of x is also the prime factor of y
(2) every factor of x is also a factor of y
i went with D, but seems missed something The answer is B because: if every prime factor x is also a prime factor of y - lets take an example: X= 30 prime factors = 2, 3, 5 y = 60 prime factors = 2, 3, 5 but x/y = 1/2 whereas if all factors of x = all factors of y that simply tells us that x is y inclusive and therefore totally divisible by y.
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Re: is x/y is an integer [#permalink]
11 Apr 2012, 13:17
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Re: If r and s are positive integers, is r/s an integer? [#permalink]
11 Apr 2012, 13:25
Bunuel
what about the word "every" - according to this i picked up numbers which satisfied this condition.
And one more point-official explanation "takes" the numbers 18 and 8, to explain the answer.
But 18 has the prime factors 2 and 3, but 8 hasn't 3 as a prime factor - what means not every factor of x is also a prime factor of y - and this contradicts with the statement
I just need to clarify -to avoid such a confusion on the exam
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Re: If r and s are positive integers, is r/s an integer? [#permalink]
11 Apr 2012, 13:28
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Re: If r and s are positive integers, is r/s an integer? [#permalink]
11 Apr 2012, 13:30
i mean this one
(2) Every prime factor of s is also a prime factor of r.
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Re: If r and s are positive integers, is r/s an integer? [#permalink]
11 Apr 2012, 13:40
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If r & 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.
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Re: If r and s are positive integers, is r/s an integer? [#permalink]
23 Aug 2012, 21:14
What if S>R? It doesn't say that R>S. It just says they are positive integers.
For first statement:
R>S = 20/10 = 2 --> Integer
S>R = 10/20 = .5 --> Not an integer
For the second statement:
R>S = 50/5 = 10 --> Integer
S>R = 5/50 = .5 --> Not an integer
That is why I picked E. Can you please explain why my reasoning is incorrect? Thanks!
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Re: If r and s are positive integers, is r/s an integer? [#permalink]
24 Aug 2012, 02:04
KAS1 wrote: What if S>R? It doesn't say that R>S. It just says they are positive integers.
For first statement:
R>S = 20/10 = 2 --> Integer
S>R = 10/20 = .5 --> Not an integer
For the second statement:
R>S = 50/5 = 10 --> Integer
S>R = 5/50 = .5 --> Not an integer
That is why I picked E. Can you please explain why my reasoning is incorrect? Thanks! For the first statement s cannot be greater than r. If every factor of s is also factor of r, then r\geq{s}. Your example, (r=10 and s=20), is not possible, because 4 is a factor of s but not a factor of r. Hope it's clear.
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Re: If a and b are positive integers, is ‘a’ a multiple of b? [#permalink]
25 Sep 2012, 11:24
ankit0411 wrote: If a and b are positive integers, is ‘a’ a multiple of b?
(1) Every prime factor of b is also a prime factor of a (2) Every factor of b is also a factor of a (1) Consider for example a = 2\cdot3=6 and b = 2^2\cdot3=12, so obviously a is not a multiple of b.If a = 12 and b = 6, then of course a is a multiple of b.Not sufficient. (2) b is a factor of itself, so it is also a factor of a, which means that a is a multiple of b.Sufficient. Answer B.
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DS : X and Y are two positive integers [#permalink]
24 Oct 2012, 23:25
Hi,
I'm trying to figure out this one.
X and Y are two positive integers. Is x divided by y an integer?
(1) All of Y's factors are also factors of X.
(2) Each prime factor of Y is also a prime factor of X.
Any pointers, please?
A, B, C, D or E?
Thanks.
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Re: DS : X and Y are two positive integers [#permalink]
24 Oct 2012, 23:33
elegan wrote: Hi,
I'm trying to figure out this one.
X and Y are two positive integers. Is x divided by y an integer?
(1) All of Y's factors are also factors of X.
(2) Each prime factor of Y is also a prime factor of X.
Any pointers, please?
A, B, C, D or E?
Thanks. 1) Y itself is a factor of Y. Hence Y is also a factor of X. Sufficient 2)Suppose X = 2 and Y = 8. Answer is No. If Y = 2 and X =8 answer is yes. Insufficient Answer is A. Kudos Please... If my post helped.
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If r and s are positive integers, is r/s an integer? [#permalink]
23 Apr 2013, 18:11
If r and s are positive integers, is \frac{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.
My doubt is this:
In (2), it seems that copies or the prime factors are no important, right? In other words, the fact that s could have a greater number of 2s than r is irrelevant. If r is \sqrt{2^2} and s is \sqrt{2^3}, we could say that every prime factor of s is also a prime factor of r, even though s has more 2s, right?
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Re: If r and s are positive integers, is r/s an integer? [#permalink]
23 Apr 2013, 18:15
danzig wrote: If r and s are positive integers, is \frac{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.
My doubt is this:
In (2), it seems that copies or the prime factors are no important, right? In other words, the fact that s could have a greater number of 2s than r is irrelevant. If r is \sqrt{2^2} and s is \sqrt{2^3}, we could say that every prime factor of s is also a prime factor of r, even though s has more 2s, right?
Merging similar topics. Please refer to the solutions above and ask if anything remains unclear.
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Re: If r and s are positive integers, is r/s an integer?
[#permalink]
23 Apr 2013, 18:15
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