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# If n is the product of 3 same prime numbers and 1 different prime numb

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7256
GMAT 1: 760 Q51 V42
GPA: 3.82
If n is the product of 3 same prime numbers and 1 different prime numb  [#permalink]

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31 Jul 2017, 01:07
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15% (low)

Question Stats:

75% (00:53) correct 25% (01:50) wrong based on 95 sessions

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If n is the product of 3 same prime numbers and 1 different prime number, then how many different factors of n are there?

A. 6
B. 8
C. 9
D. 12
E. 18

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 09 Dec 2014 Posts: 37 Re: If n is the product of 3 same prime numbers and 1 different prime numb [#permalink] ### Show Tags 31 Jul 2017, 01:23 Let p and q be the prime numbers. n= (p^3)*q Factor will be: n, 1, p, p^2, p^3, q, p*q, (p^2)*q 8 factors. Answer: B _________________ Thanks, Ramya Senior PS Moderator Joined: 26 Feb 2016 Posts: 3386 Location: India GPA: 3.12 If n is the product of 3 same prime numbers and 1 different prime numb [#permalink] ### Show Tags 31 Jul 2017, 02:42 If the number n can be represented as a product of 2 primes p and q, where p has x occurrences and q has y occurrences($$n = p^x * q^y$$), the total number of factors possible is equal to (x+1)(y+1) Coming back to the problem, the prime numbers p and q occur 3 times and 1 time respectively, the total number of factors is (1+1)(3+1) = 2*4 = 8(Option B) _________________ You've got what it takes, but it will take everything you've got Senior SC Moderator Joined: 22 May 2016 Posts: 2654 If n is the product of 3 same prime numbers and 1 different prime numb [#permalink] ### Show Tags 31 Jul 2017, 18:20 1 MathRevolution wrote: If n is the product of 3 same prime numbers and 1 different prime number, then how many different factors of n are there? A. 6 B. 8 C. 9 D. 12 E. 18 For those who haven't seen material in citation below: To find the number of factors of n, the method for the formula* mentioned above is 1. List n's prime factors raised to the correct power. Factors here are "three same prime numbers and one different prime number..." Just assign values (this formula depends on exponents) 7*7*7*13 is $$7^313^1$$ 2. List the exponents and add 1 to each 3 (+ 1) = 4 1 (+ 1) = 2 3. Multiply the resultant numbers 4*2 = 8 factors of n, 1 and n included Answer B *Bunuel, Finding the Number of Factors of an Integer, at https://gmatclub.com/forum/math-number- ... 88376.html _________________ Listen, are you breathing just a little, and calling it a life? -- Mary Oliver For practice SC questions with official explanations that were posted and moderated by the SC Team, go to SC Butler here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7256 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If n is the product of 3 same prime numbers and 1 different prime numb [#permalink] ### Show Tags 02 Aug 2017, 00:58 ==> You get $$n=(3)(3)(3)(5)$$, which becomes $$n=3^35^1$$. Thus, the number of factors of n becomes $$(3+1)(1+1)=8$$. The answer is B. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: If n is the product of 3 same prime numbers and 1 different prime numb   [#permalink] 02 Aug 2017, 00:58
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# If n is the product of 3 same prime numbers and 1 different prime numb

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