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# If the product of 5 different positive integers is less than 200, what

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If the product of 5 different positive integers is less than 200, what  [#permalink]

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20 Jun 2018, 00:48
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15% (low)

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77% (01:36) correct 23% (02:18) wrong based on 69 sessions

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[GMAT math practice question]

If the product of 5 different positive integers is less than 200, what is the greatest possible value for the largest of these 5 integers?

A. 3
B. 6
C. 7
D. 8
E. 9

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7112 Re: If the product of 5 different positive integers is less than 200, what [#permalink] ### Show Tags 20 Jun 2018, 01:44 MathRevolution wrote: [GMAT math practice question] If the product of 5 different positive integers is less than 200, what is the greatest possible value for the largest of these 5 integers? A. 3 B. 6 C. 7 D. 8 E. 9 All 5 are different positive integers, so largest has to be at least 5.. Nearest in choice is 6.. Moreover take the smallest possible value for other 4 so 1*2*3*4=24 The fifth will be <200/24.. 100/11=25/3=8+1/3.. Thus the largest will be 8 and value will be 8*1*4*3*2=192<200 D _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Intern Status: Prep Mode Joined: 16 Jan 2015 Posts: 21 Location: India GMAT 1: 630 Q48 V28 WE: Programming (Computer Software) Re: If the product of 5 different positive integers is less than 200, what [#permalink] ### Show Tags 20 Jun 2018, 01:53 3 1 a*b*c*d*e < 200 Let us consider 'e' is largest integer Since all are positive integers, for 'e' to be largest --> a,b,c,d should be smallest. Given that all integers different, 4 lowest positive integers are 1,2,3,4 1*2*3*4*e < 200 e < (200/24) e < 8.33 Since 'e' is highest integer, answer is 8 Senior Manager Joined: 04 Aug 2010 Posts: 310 Schools: Dartmouth College Re: If the product of 5 different positive integers is less than 200, what [#permalink] ### Show Tags 20 Jun 2018, 02:03 1 MathRevolution wrote: [GMAT math practice question] If the product of 5 different positive integers is less than 200, what is the greatest possible value for the largest of these 5 integers? A. 3 B. 6 C. 7 D. 8 E. 9 To MAXIMIZE the largest integer, MINIMIZE the other four integers. Since the integers must be positive and distinct, the smallest possible option for the other four integers is as follows: 1*2*3*4 = 24. We can PLUG IN THE ANSWERS, which represent the value of the largest integer. Of the five answer choices -- 3, 6, 7, 8, 9 -- the largest that can be multiplied by 24 to yield a product less than 200 is 8: 24*8 = 192. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4314 Location: United States (CA) Re: If the product of 5 different positive integers is less than 200, what [#permalink] ### Show Tags 21 Jun 2018, 16:10 MathRevolution wrote: [GMAT math practice question] If the product of 5 different positive integers is less than 200, what is the greatest possible value for the largest of these 5 integers? A. 3 B. 6 C. 7 D. 8 E. 9 To maximize the largest of the 5 integers, we minimize the values of the smallest 4 integers. Since they are positive and are different from each other, they must be 1, 2, 3, and 4. The product of the first four integers is 1 x 2 x 3 x 4 = 24. The largest integer that could multiply 24 and produce a product that is less than 200 is 8, since 24 x 8 = 192. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6661 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If the product of 5 different positive integers is less than 200, what [#permalink] ### Show Tags 21 Jun 2018, 23:45 => The greatest possible value of the largest of the integers occurs when the other integers are as small as possible. In other words, the other four integers should be $$1,2,3$$, and $$4$$. We try different values for the fifth integer: $$1*2*3*4*5 = 120$$ $$1*2*3*4*6 = 144$$ $$1*2*3*4*7 = 168$$ $$1*2*3*4*8 = 192$$ $$1*2*3*4*9 = 216$$ The largest product that is less than $$200$$ occurs when the fifth integer is $$8$$. Thus, the greatest possible value of the largest integer is $$8$$. Therefore, the answer is D. Answer: D _________________ 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$99 for 3 month Online Course"
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Joined: 03 Feb 2016
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Location: China
Re: If the product of 5 different positive integers is less than 200, what  [#permalink]

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02 Aug 2018, 00:32
This is how i solved it:
take prime factors of 200 = 2^3 * 5^2
look at the given options - you can A,B,C,E because with the prime factors - it s not possible.
So it is 8
Re: If the product of 5 different positive integers is less than 200, what &nbs [#permalink] 02 Aug 2018, 00:32
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