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03 Nov 2023, 22:29
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practice question from MBAdotcom.
Issue: What if S is larger than r? That will give us a fraction and not an integer.
Q: "If r and s are positive integers, is r over 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.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
Provided explanation with the question:
Arithmetic | Properties of numbers
(1) The integer s is by definition a factor of itself. From this, every factor of s is also a factor of r. Therefore, r over s must be an integer; SUFFICIENT.
(2) From this, by example, if r = 18 and s = 6, then 6 has the prime factors 2 and 3, each of which is also a factor of 18, and r over s equals eighteen sixths, which is an integer. However, if r = 18 and s = 8, then r has the prime factors 2 and 3, and s has a prime factor 2, which satisfies this condition. Even though in this case the prime factor of s is a prime factor of r, r over s equals eighteen eighths, which is not an integer; NOT sufficient.
The correct answer is A; statement 1 alone is sufficient."
again, my concern is, what if S>R?
Issue: What if S is larger than r? That will give us a fraction and not an integer.
Q: "If r and s are positive integers, is r over 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.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
Provided explanation with the question:
Arithmetic | Properties of numbers
(1) The integer s is by definition a factor of itself. From this, every factor of s is also a factor of r. Therefore, r over s must be an integer; SUFFICIENT.
(2) From this, by example, if r = 18 and s = 6, then 6 has the prime factors 2 and 3, each of which is also a factor of 18, and r over s equals eighteen sixths, which is an integer. However, if r = 18 and s = 8, then r has the prime factors 2 and 3, and s has a prime factor 2, which satisfies this condition. Even though in this case the prime factor of s is a prime factor of r, r over s equals eighteen eighths, which is not an integer; NOT sufficient.
The correct answer is A; statement 1 alone is sufficient."
again, my concern is, what if S>R?
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03 Nov 2023, 22:35
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Is this the question? There is a pretty long discussion. 😇
https://gmatclub.com/forum/if-r-and-s-a ... 28005.html
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https://gmatclub.com/forum/if-r-and-s-a ... 28005.html
Posted from my mobile device
03 Nov 2023, 22:43
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As per statement 1, If every factor of s is also a factor of r, it should mean that both the numbers should be equal. For example, if r =10 and s=5, then r will have 10 as an additional factor, which is not possible. Likewise, if s=10 and r=5, that case is also not possible. Hence, both numbers should be same and r/s will yield an integer. Statement 1 is sufficient.
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Posted from my mobile device
