gander123 wrote:Hey,
QDS03324 GMAT Prep Question Pack 1:
"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."
OA:
A
OA Explanation for (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/s, must be an integer; SUFFICIENT.
For the sake of shortness, I leave the official answer for statement (2) out here.
My Questions:
1. To evaluate statement (1) I initially chose r = 6 (containing factors 2 and 3) and s = 18 containing factors 2 and 3, 3). In this case. 6/18 = 1/3 which certainly is no integer. The only plausible explanation for the wrongness of my numbers is that I did not choose two integers with the same
number of factors.
2. So does the phrasing
every factor
here mean "the same number/amount of" factors?
I would repeat this mistake thousands of times, since it really isnt quite obvious that statement (1) meant the same amount of factors..
What would you do ?
cheers,
Tobi
In statement 1, r=6 and s=18 do not satisfy the condition that
EVERY factor of s is also a factor of r.
For example, 9 and 18 are factors of s=18 but are NOT factors of r=6.
Statement 1: Every factor of s is also a factor of r.
For EVERY factor of s to be a factor of r, S ITSELF must be a factor of r.
It is not necessary that r and s have the same number of factors.
To illustrate:
If r=18 and s=6, every factor of s (1, 2, 3, 6) is also a factor of r (whose factors are 1, 2, 3, 6, 9, 18), but r has more factors than s.
Since s itself must be a factor of r, r/s must be an integer.
SUFFICIENT.
Statement 2: Every prime factor of s is also a prime factor of r.
Case 1: r=18 and s=6.
The prime factors of r=18 are 2 and 3.
The prime factors of s=6 are 2 and 3.
Thus, every prime factor of s is also a prime factor of r.
In this case, r/s = 18/6 = 3, which is an integer.
Case 2: r=6 and s=18.
The prime factors of r=6 are 2 and 3.
The prime factors of s=18 are 2 and 3.
Thus, every prime factor of s is also a prime factor of r.
In this case, r/s = 6/18 = 1/3, which is NOT an integer.
INSUFFICIENT.
The correct answer is
A.
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