An integer n that is greater than 1 is said to be "prime-sat

I could not understand this question even. I try to practice and learn as many problems as I can. But every time there is something that I don't know about the new question. Can you tell me what should I do to improve my quant score. Really disheartened.... Many times I need to remember the whole solution to solve the same type of question again

Great Question.
Here is what i did in this one =>
If n is to be a Saturated prime -> All prime factors of n must be less than equal to √n
Start with option E=>
75=> √75=8.something
75=>3*5^2
Clearly both 3 and 5 are less than 8.something
Hence E.

We will find the largest prime factor of each answer choice. If the largest prime factor of the number is greater than the square root of the number, then the number is NOT prime saturated, since by definition no prime factor of the number is greater than or equal to its square root.

Furthermore, instead of comparing the largest prime factor and the square root of the number, we will compare the square of the largest prime factor and square of the square root of the number, i.e., the number itself. That is because if two numbers, x and y, are positive, √x > √y implies x > y.

A) 6

The largest prime factor of 6 is 3. Since 3^2 = 9 is greater than (√6)^2 = 6, 6 is NOT prime saturated.

B) 35

The largest prime factor of 35 is 7. Since 7^2 = 49 is greater than (√35)^2 = 35, 35 is NOT prime saturated.

C) 46

The largest prime factor of 46 is 23. Since 23^2 is greater than (√46)^2 = 46, 46 is NOT prime saturated.

D) 66

The largest prime factor of 66 is 11. Since 11^2 = 121 is greater than (√66)^2 = 66, 66 is NOT prime saturated.

E) 75

The largest prime factor of 75 is 5. Since 5^2 = 25 is NOT greater than (√75)^2 = 75, 75 IS prime saturated.

Answer: E

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