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

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Joined: 17 Oct 2008
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A number is said to be prime saturated if the product of all the diffe  [#permalink]

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17 Oct 2008, 10:21
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45% (medium)

Question Stats:

67% (02:09) correct 33% (01:58) wrong based on 531 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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Posts: 58390
Re: A number is said to be prime saturated if the product of all the diffe  [#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 if the product of all the diffe  [#permalink]

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19 Oct 2008, 11:44
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5
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?

Cheers
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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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19 Dec 2010, 06:51
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unbelievable thanks a lot man
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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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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 the diffe  [#permalink]

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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. $$95 =>5*19$$

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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