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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-number-is-said-to-be-prime-saturated-if-the-product-of-all-106511.html
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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 17 Oct 2008, 12:42
Check another recent post on the same question.
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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, 05:31
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amychen77 wrote:
A positive integer n 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

Clearly D
96 has more number of smaller prime factor thats the clue !!
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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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4
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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New post 26 Apr 2015, 05:31
5
5
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


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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-number-is-said-to-be-prime-saturated-if-the-product-of-all-106511.html

Similar question to practice: an-integer-n-that-is-greater-than-1-is-said-to-be-prime-sat-159908.html
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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 24 Jul 2018, 01:07
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Re: A number is said to be prime saturated if the product of all the diffe &nbs [#permalink] 24 Jul 2018, 01:07
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