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A number is said to be prime saturated if the product of all the diffe

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A number is said to be prime saturated if the product of all the diffe  [#permalink]

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New post 17 Oct 2008, 10:21
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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
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Re: A number is said to be prime saturated if the product of all the diffe  [#permalink]

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New post 18 Dec 2010, 14:36
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ajit257 wrote:
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


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.

Hope it's clear.
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Re: A number is said to be prime saturated if the product of all the diffe  [#permalink]

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New post 19 Oct 2008, 11:44
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Hi guys,

IMO: D

A prime factors are 3 and 11. 33<sqrt(99)? no

B prime factors are 2 and 7. 14<sqrt(98)? no

C prime number. its sqrt is never greater than itself

D A prime factors are 2 and 6. 6<sqrt(96)? yes

E prime factors are 5 and 19. 45<sqrt(95)? no

OA?

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Re: A number is said to be prime saturated if the product of all the diffe  [#permalink]

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Re: A number is said to be prime saturated if the product of all the diffe  [#permalink]

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New post 14 Feb 2011, 19:44
96 = 3 * 32 = 3 * 2^5

Answer is D.
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Re: A number is said to be prime saturated if the product of all the diffe  [#permalink]

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New post 11 Dec 2018, 09:35
amychen77 wrote:
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


Given prime saturated is the product of all the different positive prime factors of \(n\) which is less than the \(\sqrt{n}\).

Checking the answer choices; the highest value is \(99\). \(\sqrt{99}\) is more than \(9\) and less than \(10\).

Lowest value is \(95\). \(\sqrt{95}\) is more than \(9\) and less than \(10\).

Hence the square root of all answer choices are between \(9\) and \(10\).

A. \(99 = 3*3*11\) \(=> 3*11 = 33\)

B. \(98 = 2*7*7\) \(=> 2*7 = 14\)

C. \(97 => 1* 97\)

D. \(96 = 2^5*3\) \(=> 2*3 = 6\). \(=>\) Less than \(\sqrt{96}\).

E. \(95 =>5*19\)

Answer D
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Re: A number is said to be prime saturated if the product of all the diffe   [#permalink] 11 Dec 2018, 09:35
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