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kiran120680
Moderator - Masters Forum
Joined: 18 Feb 2019
Last visit: 27 Jul 2022
Posts: 706
Given Kudos: 276
Location: India
Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
GMAT 1: 460 Q42 V13
GPA: 3.6
09 Jun 2019, 10:01
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
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Question Stats:
69% (02:14) correct
31%
(02:14)
wrong
based on 688
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For every positive integer p, f(p) represents the product of first p positive multiples of 3. How many prime numbers divide f(30)?
A. 2
B. 5
C. 8
D. 10
E. 13
A. 2
B. 5
C. 8
D. 10
E. 13
10 Jun 2019, 05:12
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kiran120680
f(p) represents the product of first p positive multiples of 3. So f(30)= (3*1)(3*2)(3*3)(3*4)..(3*29)(3*30)...
So, the prime numbers till 30 will be factor of f(30)..
Numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29---- 10 in number
D
General Discussion
23 Aug 2020, 16:53
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1st) find the 30th Multiple of 3 so you know the Range of the Multiples of 3 included in f(p)
the 30th Multiple of 3 = 30 * 3 = 90
thus, f(p) = 3 * 6 * 9 * 12 ...... * 87 * 90
2nd) To see which Prime Numbers are included in this Product Chain, keep Multiplying the 1st Prime Numbers TIMES 3 in Ascending Order until you reach a Result greater than 90 (which will therefore not be a Prime Factor included in the Product Chain)
Since 17 * 3 = 51
every Prime No. from 2 - 17 is a Prime Factor in the product chain.
19 * 3 = 57
23 * 3 = 69
29 * 3 = 87
any prime number > 30 will NOT be included.
All the Prime Numbers from 2 thru 29, inclusive:
2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29
Answer: 10 Prime Numbers
the 30th Multiple of 3 = 30 * 3 = 90
thus, f(p) = 3 * 6 * 9 * 12 ...... * 87 * 90
2nd) To see which Prime Numbers are included in this Product Chain, keep Multiplying the 1st Prime Numbers TIMES 3 in Ascending Order until you reach a Result greater than 90 (which will therefore not be a Prime Factor included in the Product Chain)
Since 17 * 3 = 51
every Prime No. from 2 - 17 is a Prime Factor in the product chain.
19 * 3 = 57
23 * 3 = 69
29 * 3 = 87
any prime number > 30 will NOT be included.
All the Prime Numbers from 2 thru 29, inclusive:
2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29
Answer: 10 Prime Numbers
