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

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Joined: 28 Aug 2010
Posts: 231
A number is said to be prime saturated if the product of all  [#permalink]

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18 Dec 2010, 14:24
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Difficulty:

45% (medium)

Question Stats:

68% (01:35) correct 32% (01:26) wrong based on 344 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

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Ajit

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Re: A number is said to be prime saturated  [#permalink]

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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.

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  [#permalink]

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19 Dec 2010, 06:51
1

unbelievable thanks a lot man
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Re: A number is said to be prime saturated  [#permalink]

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

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

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05 Feb 2018, 11:00
Bunuel wrote:
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.

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.

How do you know that n is 3?
Re: A number is said to be prime saturated if the product of all &nbs [#permalink] 05 Feb 2018, 11:00
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