swerve wrote: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

So, n is prime saturated if the largest prime factor of n < √n
If we square both sides of the inequality, we get: n is prime saturated if (the largest prime factor of n)² < n

A. 6 = (2)(3) ---> 3² > 6 n is NOT PRIME SATURATED
B. 35 = (5)(7) ---> 7² > 35 n is NOT PRIME SATURATED
C. 46 = (2)(23) ---> 23² > 46 n is NOT PRIME SATURATED
D. 66 = (2)(3)(11) ---> 11² > 66 n is NOT PRIME SATURATED
E. 75 = (3)(5)(5) ---> 5² < 75 n IS PRIME SATURATED

Answer: E

Cheers,
Brent

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