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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
A number is said to be prime saturated if the product of all the diffe
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23 Dec 2022, 09:12
23 Dec 2022, 09:12
Expert Reply
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Question Stats:
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100% (02:01) wrong based on 4 sessions
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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 prime saturated integer ?
A. 99
B. 98
C. 97
D. 96
E. 95
A. 99
B. 98
C. 97
D. 96
E. 95
Re: A number is said to be prime saturated if the product of all the diffe
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27 Dec 2022, 01:19
27 Dec 2022, 01:19
1
Expert Reply
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 then 9, so this number should have only 2-s, only 3-s, only 5-s, or only 2-s and 3-s as its primes. Only 96 satisfies this.
Answer: D.
Or just make prime factorization of all numbers:
A. 99 = 3^2*11 --> 3*11=33>9;
B. 98 = 2*7^2 --> 2*7=14>9;
C. 97 = prime number>9;
D. 96 = 2^5*3 --> 2*3=6<9;
E. 95 = 5*19 --> 5*19=95>9.
Answer: D.
Or just make prime factorization of all numbers:
A. 99 = 3^2*11 --> 3*11=33>9;
B. 98 = 2*7^2 --> 2*7=14>9;
C. 97 = prime number>9;
D. 96 = 2^5*3 --> 2*3=6<9;
E. 95 = 5*19 --> 5*19=95>9.
gmatclubot
Re: A number is said to be prime saturated if the product of all the diffe [#permalink]
27 Dec 2022, 01:19
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