swerve wrote: ↑Thu Nov 28, 2019 11:09 am
An integer n that is greater than 1 is said to be "prime-saturated" if it has no prime factor greater than or equal to n√n. Which of the following integers is prime saturated?
A. 6
B. 35
C. 46
D. 66
E. 75
The OA is
E
Source: GMAT Prep
If p is the largest prime factor of n, in order of n to be "prime-saturated", we need to have p ≤ √n. In other words, we want p^2 ≤ n. Now, let’s check the given choices:
A. 6
6 = 2 x 3, but 3^2 = 9, which is greater than 6. So choice A is not the correct answer.
B. 35
35 = 5 x 7, but 7^2 = 49, which is greater than 35. So choice B is not the correct answer.
C. 46
46 = 2 x 23, but 23^2 > 35. So choice C is not the correct answer.
D. 66
66 = 2 x 3 x 11, but 11^2 = 121, which is greater than 66. So choice D is not the correct answer.
This leaves us with choice E as the correct answer. However, let’s verify it is indeed the correct answer anyway.
E. 75
75 = 3 x 5 x 5 and 5^2 = 25 is indeed less than 75.
Answer: E 
