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23 Feb 2012, 08:13
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
63% (01:04) correct
37%
(01:13)
wrong
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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.
(1) Every factor of s is also a factor of r.
(2) Every prime factor of s is also a prime factor of r.
23 Feb 2012, 08:26
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If r and s are positive integers, is r/s an integer?
(1) Every factor of s is also a factor of r. If every factor of s is also factor of r, then in fraction r/s, s will just be reduced and we get an integer. Sufficient.
(2) Every prime factor of s is also a prime factor of r. The powers of prime factors of s could be higher than powers of prime factors of r. eg 25/125=1/5 not an integer. Not sufficient.
Answer: A.
Hope it's clear.
(1) Every factor of s is also a factor of r. If every factor of s is also factor of r, then in fraction r/s, s will just be reduced and we get an integer. Sufficient.
(2) Every prime factor of s is also a prime factor of r. The powers of prime factors of s could be higher than powers of prime factors of r. eg 25/125=1/5 not an integer. Not sufficient.
Answer: A.
Hope it's clear.
24 Aug 2012, 02:04
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KAS1
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 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.
