GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Aug 2018, 03:51

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6040
GMAT 1: 760 Q51 V42
GPA: 3.82
If the product of 5 different positive integers is less than 200, what  [#permalink]

### Show Tags

20 Jun 2018, 01:48
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:41) correct 19% (02:13) wrong based on 63 sessions

### HideShow timer Statistics

[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

_________________

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" "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: 6556 Re: If the product of 5 different positive integers is less than 200, what [#permalink] ### Show Tags 20 Jun 2018, 02:44 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: 17 Location: India WE: Programming (Computer Software) Re: If the product of 5 different positive integers is less than 200, what [#permalink] ### Show Tags 20 Jun 2018, 02:53 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 Manager Joined: 04 Aug 2010 Posts: 237 Schools: Dartmouth College Re: If the product of 5 different positive integers is less than 200, what [#permalink] ### Show Tags 20 Jun 2018, 03:03 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: 3182 Location: United States (CA) Re: If the product of 5 different positive integers is less than 200, what [#permalink] ### Show Tags 21 Jun 2018, 17:10 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: 6040 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 22 Jun 2018, 00:45 => 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"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 03 Feb 2016
Posts: 11
Location: China
Re: If the product of 5 different positive integers is less than 200, what  [#permalink]

### Show Tags

02 Aug 2018, 01:32
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, 01:32
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.