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# How many integers between 18 and 3399 are multiples of 17?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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How many integers between 18 and 3399 are multiples of 17?  [#permalink]

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13 Feb 2019, 01:56
00:00

Difficulty:

35% (medium)

Question Stats:

60% (01:56) correct 40% (02:20) wrong based on 43 sessions

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[GMAT math practice question]

How many integers between $$18$$ and $$3399$$ are multiples of $$17$$?

$$A. 198$$
$$B. 199$$
$$C. 200$$
$$D. 201$$
$$E. 202$$

_________________

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" Director Joined: 18 Jul 2018 Posts: 748 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: How many integers between 18 and 3399 are multiples of 17? [#permalink] ### Show Tags 13 Feb 2019, 02:01 First integer,a = 34, difference, d = 17. 3400 is divisible by 17, as 17*200 Then last multiple = 3400-17 = 3383. 3383 = 34+(n-1)17 n-1 = (3383-34)/17 = 197. n = 198 A is the answer Posted from my mobile device _________________ Press +1 Kudo If my post helps! Manager Joined: 07 Aug 2017 Posts: 63 Location: India GPA: 4 WE: Information Technology (Consulting) Re: How many integers between 18 and 3399 are multiples of 17? [#permalink] ### Show Tags 13 Feb 2019, 02:28 Range = 3399-18+1=3381 Number of multiples of 17 in the range = 3381/17=198.88 = 198 multiples ---------------------------- Kudos if helpful! CEO Joined: 12 Sep 2015 Posts: 3507 Location: Canada Re: How many integers between 18 and 3399 are multiples of 17? [#permalink] ### Show Tags 13 Feb 2019, 07:44 Top Contributor MathRevolution wrote: [GMAT math practice question] How many integers between $$18$$ and $$3399$$ are multiples of $$17$$? $$A. 198$$ $$B. 199$$ $$C. 200$$ $$D. 201$$ $$E. 202$$ Another approach: Let's list the multiples of 17 that are between 18 and 3399 : 34 = 2(17) 51 = 3(17) 68 = 4(17) 85 = 5(17) . . . 3383 = 199(17) So, the number of multiples of 17 is EQUAL to the number of integers from 2 to 199 inclusive ASIDE: A nice rule says: the number of integers from x to y inclusive equals y - x + 1 So, the number of integers from 2 to 199 inclusive = 199 - 2 + 1 = 198 Answer: A Cheers, Brent _________________ Test confidently with gmatprepnow.com Senior Manager Joined: 04 Aug 2010 Posts: 383 Schools: Dartmouth College Re: How many integers between 18 and 3399 are multiples of 17? [#permalink] ### Show Tags 13 Feb 2019, 08:40 MathRevolution wrote: [GMAT math practice question] How many integers between $$18$$ and $$3399$$ are multiples of $$17$$? $$A. 198$$ $$B. 199$$ $$C. 200$$ $$D. 201$$ $$E. 202$$ 17*200 = 3400 = multiple of 17. 3399 is one less than a multiple of 17 and thus cannot itself be a multiple of 17. Since neither endpoint is a multiple of 17, we can simply divide 17 into the difference between the two endpoints: $$\frac{3399-18}{17} = \frac{3381}{17} = 198\frac{15}{17}$$. Since 17 divides into the difference 198 times, there are 198 multiples of 17 between the two endpoints. _________________ 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. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7087 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: How many integers between 18 and 3399 are multiples of 17? [#permalink] ### Show Tags 15 Feb 2019, 01:20 => $$18 = 17*1 + 1, 34 = 17*2$$ is the least multiple of $$17$$ greater than $$18$$. $$3399 = 17*199 + 16, 3383 = 17*199$$ is the greatest multiple of $$17$$ less than $$3399.$$ Thus, the multiples of $$17$$ between $$18$$ and $$3399$$ are $$34=17*2, … , 3383 = 17*199.$$ There are $$198 = (199 – 2) + 1$$ of these numbers as they are in one-to-one correspondence with the integers between $$2$$ and $$199$$, inclusive. Therefore, the answer is A. Answer: A _________________ 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: How many integers between 18 and 3399 are multiples of 17?  [#permalink]

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15 Feb 2019, 18:21
MathRevolution wrote:
[GMAT math practice question]

How many integers between $$18$$ and $$3399$$ are multiples of $$17$$?

$$A. 198$$
$$B. 199$$
$$C. 200$$
$$D. 201$$
$$E. 202$$

Notice that 17 is a multiple of 17. However, since 17 < 18, we need to go to the next one, 34, as the first multiple of 17 that is within the range of 18 to 3399. Similarly, notice that 3400 is a multiple of 17. However, since 3400 > 3399, we need to go to the previous one, 3383, as the final multiple of 17 that is within the range of 18 to 3399. Therefore, the number of multiples of 17 within the given range is:

(3383 - 34)/17 + 1 = 197 + 1 = 198

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Re: How many integers between 18 and 3399 are multiples of 17?   [#permalink] 15 Feb 2019, 18:21
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