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# Problem Solving Pack 4, Question 4 If (2^n)(3^k)(5^12)...

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EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
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Joined: 19 Dec 2014
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GMAT 1: 800 Q51 V49
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Problem Solving Pack 4, Question 4 If (2^n)(3^k)(5^12)...  [#permalink]

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Updated on: 24 Nov 2015, 00:09
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:40) correct 12% (03:01) wrong based on 84 sessions

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QUANT 4-PACK SERIES Problem Solving Pack 4 Question 4 If (2^n)(3^k)(5^8)...

If ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) is equal to one percent of $$60^{10}$$ , then what is the value of N – K?

A) 7
B) 8
C) 12
D) 14
E) 15

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This question is part of the Quant 4-Pack series

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# Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Originally posted by EMPOWERgmatRichC on 19 Nov 2015, 16:51. Last edited by EMPOWERgmatRichC on 24 Nov 2015, 00:09, edited 1 time in total. Senior Manager Joined: 28 Feb 2014 Posts: 294 Location: United States Concentration: Strategy, General Management Re: Problem Solving Pack 4, Question 4 If (2^n)(3^k)(5^12)... [#permalink] ### Show Tags 19 Nov 2015, 17:19 1 If ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) is equal to one percent of $$60^{10}$$ , then what is the value of N – K? A) 7 B) 8 C) 12 D) 14 E) 15 60=(2^2)*3*5 ($$1/100$$)*($$(2^2)*3*5$$)^100= ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) ($$2^{20}$$)*($$3^{10}$$)*($$5^{10}$$)= ($$2^{N+2}$$) ($$3^{K}$$) ($$5^{10}$$) N+2=20 N=18 K=10 18-10=8 Answer: B CEO Joined: 20 Mar 2014 Posts: 2635 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Problem Solving Pack 4, Question 4 If (2^n)(3^k)(5^12)... [#permalink] ### Show Tags 23 Nov 2015, 08:28 1 EMPOWERgmatRichC wrote: QUANT 4-PACK SERIES Problem Solving Pack 4 Question 4 If (2^n)(3^k)(5^12)... If ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) is equal to one percent of $$60^{10}$$ , then what is the value of N – K? A) 7 B) 8 C) 12 D) 14 E) 15 48 Hour Window Answer & Explanation Window Earn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4-Pack series Scroll Down For Official Explanation Given, ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) = 1% of $$60^{10}$$= $$60^8$$ ---> ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) = $$60^8$$ =$$[(2^2)*(3)*5]^8$$ = $$[(2^{16})*(3^8)*5^8]$$---> n=16 and m=8 , giving n-k=8. B is the correct answer. Current Student Joined: 28 Jul 2014 Posts: 13 Re: Problem Solving Pack 4, Question 4 If (2^n)(3^k)(5^12)... [#permalink] ### Show Tags 23 Nov 2015, 08:45 1 (2^N) * (3^K)*(5^8) = (10^-2)*(60^10) RHS = (2*5)^-2 * (2^2*3*5)^10 = (2^-2)*(5^-2)*(2^20)*(3^10)*(5^10) = (2^18)*(3^10)*(5^8) N = 18, K = 10; N-K = 8 =>B Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4224 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: Problem Solving Pack 4, Question 4 If (2^n)(3^k)(5^12)... [#permalink] ### Show Tags 23 Nov 2015, 11:05 1 EMPOWERgmatRichC wrote: QUANT 4-PACK SERIES Problem Solving Pack 4 Question 4 If (2^n)(3^k)(5^12)... If ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) is equal to one percent of $$60^{10}$$ , then what is the value of N – K? A) 7 B) 8 C) 12 D) 14 E) 15 ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) = $$10$$% of $$60^{10}$$ ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) = $$60^{8}$$ To make the highlighted part a factor of 60, we must have - ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) = $$60^{8}$$ ($$2^{16}$$) ($$3^{8}$$) ($$5^{8}$$) = $$60^{8}$$ since - Since 60 = $$2^{2}$$ ( $$3$$)( $$5$$) Now we get N = 16 and K = 8 So, N - K = 8 _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12882 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Problem Solving Pack 4, Question 4 If (2^n)(3^k)(5^8)... [#permalink] ### Show Tags 24 Nov 2015, 00:26 1 EMPOWERgmatRichC wrote: QUANT 4-PACK SERIES Problem Solving Pack 4 Question 4 If (2^n)(3^k)(5^8)... If ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) is equal to one percent of $$60^{10}$$ , then what is the value of N – K? A) 7 B) 8 C) 12 D) 14 E) 15 Hi All, This question is based on the concept of Prime Factorization (the idea that every positive integer greater than 1 is either a prime number OR the product of prime numbers). To start, we're told that ($$2^{N}$$) ($$3^{K}$$) ($$5)^{8}$$) = $$60^{10}$$ / 100 The 'right side' of the equation can be rewritten as... $$(2x2x3x5)^{10}$$/ (2x2x5x5) = $$(2)^{18}$$ $$(3)^{10}$$ $$(5^{8}$$ When this calculation is substituted into the larger equation, we have... ($$2^{N}$$) ($$3^{K}$$) ($$5^{8}$$) = $$(2)^{18}$$ $$(3)^{10}$$ $$(5)^{8}$$ 'Canceling out' the common terms leaves us.... N = 18 and K = 10 Thus, N - K = 18 - 10 = 8 Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: Problem Solving Pack 4, Question 4 If (2^n)(3^k)(5^12)...  [#permalink]

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# Problem Solving Pack 4, Question 4 If (2^n)(3^k)(5^12)...

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