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# 693 and n have the same prime factors and n is a multiple of 693 that

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6613
GMAT 1: 760 Q51 V42
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693 and n have the same prime factors and n is a multiple of 693 that  [#permalink]

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28 Jun 2018, 02:37
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Difficulty:

45% (medium)

Question Stats:

60% (01:20) correct 40% (01:13) wrong based on 74 sessions

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[GMAT math practice question]

$$693$$ and $$n$$ have the same prime factors and $$n$$ is a multiple of $$693$$ that is greater than $$693$$. What is the smallest possible value of $$\frac{n}{693}$$?

$$A. 2$$
$$B. 3$$
$$C. 5$$
$$D. 7$$
$$E. 11$$

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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" Senior Manager Joined: 04 Aug 2010 Posts: 310 Schools: Dartmouth College 693 and n have the same prime factors and n is a multiple of 693 that [#permalink] ### Show Tags Updated on: 28 Jun 2018, 05:06 MathRevolution wrote: [GMAT math practice question] $$693$$ and $$n$$ have the same prime factors and $$n$$ is a multiple of $$693$$ that is greater than $$693$$. What is the smallest possible value of $$\frac{n}{693}$$? $$A. 2$$ $$B. 3$$ $$C. 5$$ $$D. 7$$ $$E. 11$$ $$693 = 3^2*7*11$$ Since n must have the same prime factors as 693 but must be greater than 693, the least possible option for $$n = 693 * 3$$. Thus, least possible value of $$\frac{n}{693} = \frac{(693*3)}{693} = 3$$. _________________ 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. Originally posted by GMATGuruNY on 28 Jun 2018, 02:50. Last edited by GMATGuruNY on 28 Jun 2018, 05:06, edited 1 time in total. Senior PS Moderator Joined: 26 Feb 2016 Posts: 3325 Location: India GPA: 3.12 693 and n have the same prime factors and n is a multiple of 693 that [#permalink] ### Show Tags 28 Jun 2018, 04:15 MathRevolution wrote: [GMAT math practice question] $$693$$ and $$n$$ have the same prime factors and $$n$$ is a multiple of $$693$$ that is greater than $$693$$. What is the smallest possible value of $$\frac{n}{693}$$? $$A. 2$$ $$B. 3$$ $$C. 5$$ $$D. 7$$ $$E. 11$$ If the numbers n and 693 have the same prime factors and n is a multiple of 693, the smallest value of $$\frac{n}{693}$$ must be the smallest prime factor of 693. 693 when prime-factorized gives $$3^2*7*11$$. The minimum value of n is $$3*693$$(as n and 693 have same prime numbers) Therefore, the smallest value of $$\frac{n}{693}$$ is $$\frac{3*693}{693} = 3$$(Option B) _________________ You've got what it takes, but it will take everything you've got Math Expert Joined: 02 Aug 2009 Posts: 7096 693 and n have the same prime factors and n is a multiple of 693 that [#permalink] ### Show Tags 28 Jun 2018, 04:28 MathRevolution wrote: [GMAT math practice question] $$693$$ and $$n$$ have the same prime factors and $$n$$ is a multiple of $$693$$ that is greater than $$693$$. What is the smallest possible value of $$\frac{n}{693}$$? $$A. 2$$ $$B. 3$$ $$C. 5$$ $$D. 7$$ $$E. 11$$ $$693$$ and $$n$$ have the same prime factors and $$n$$ is a multiple of $$693$$ that is greater than $$693$$.... when will n and 693 have the same prime factors :- when n is multiple of 693 and its prime factors so lowest value of $$\frac{n}{693}$$ will come from lowest value of n and will be equal to the smallest prime number of 693, which is 3. lets solve it also 693 is clearly a multiple of 3 and there are NO other odd prime numbers < 3..... so n lowest value but > 693 is 693*3 therefore $$\frac{n}{693}=\frac{3*693}{693}=3$$ _________________ 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6613 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: 693 and n have the same prime factors and n is a multiple of 693 that [#permalink] ### Show Tags 01 Jul 2018, 17:12 => Since $$693 = 3^2*7*11$$, the smallest integer multiple of $$693$$ that is greater than $$693$$ with prime factors $$3, 7$$ and $$11$$ only is $$n = 693*3$$. Thus, $$\frac{n}{693} = \frac{( 693 * 3 )}{693} = 3.$$ Therefore, 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$99 for 3 month Online Course"
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Re: 693 and n have the same prime factors and n is a multiple of 693 that  [#permalink]

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02 Jul 2018, 08:42
MathRevolution wrote:
[GMAT math practice question]

$$693$$ and $$n$$ have the same prime factors and $$n$$ is a multiple of $$693$$ that is greater than $$693$$. What is the smallest possible value of $$\frac{n}{693}$$?

$$A. 2$$
$$B. 3$$
$$C. 5$$
$$D. 7$$
$$E. 11$$

Let us express 693 as a product of prime powers: 693 = 9 x 77 = 3^2 x 7 x 11. The prime factors of 693 are 3, 7 and 11. Since n has the same prime factors as 693, n also has prime factors of 3, 7, 11. Since n is a multiple of 693 that is greater than 693, the smallest value that n can be is 3 x 693 and thus the smallest possible value of n/693 is (3 x 693)/693 = 3.

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Re: 693 and n have the same prime factors and n is a multiple of 693 that &nbs [#permalink] 02 Jul 2018, 08:42
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