A Number is Said to be Prime Saturated if the Product of all the Different GMAT Problem Solving

Question: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. what is the greatest two digit saturated integer?

1. 99
2. 98
3. 97
4. 96
5. 95

“A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. what is the greatest two digit saturated integer?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution (1):

The square roots of all numbers from answer choices are between 9 and 10, so the product of primes of the number we are looking should be less than 89, so this number should have only 2-s, only 3-s, only5-s, or only only 2-s and 3-s as its primes. Only 96 satisfies this.

Correct option: D

Approach Solution (2):

Just make prime factorization of all the numbers:

99 = 3^2 * 11 = 3 * 11 = 33 > 9

98 = 2 * 7^2 = 2 * 7 = 14 > 9

97 = prime number > 9

96 = 2^5 * 3 = 2 * 3 = 6 < 9

95 = 5 * 19 = 5 * 19 = 95 > 9

Correct option: D

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