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

Question

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

Bunuel · Accepted Answer

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.

JohnLewis1980 · Answer

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

Carcass · Answer

your explenation are ALWAYS straightforward...........in each post or reply. unbelievable

thanks a lot man

subhashghosh · Answer

96 = 3 * 32 = 3 * 2^5

Answer is D.

sashiim20 · Answer

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

ManifestDreamMBA · Answer

All numbers are less than 100, so square root should be less than 10. Looking for product of primes which is less than 10
A) 99 = 9 * 11 = 99
B) 98 = 2 * 7^2 = 2*7 = 14
C) 97 = 1*97
 D) 96 = 3 * 2^5 = 2*3 = 6  
E) 95 = 5 * 19 = 95

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards