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# How many multiples of 33 lie between 101 and 1,000, inclusive?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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How many multiples of 33 lie between 101 and 1,000, inclusive?  [#permalink]

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20 Sep 2018, 01:04
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86% (01:27) correct 14% (01:33) wrong based on 79 sessions

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[Math Revolution GMAT math practice question]

How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive?

$$A. 24$$
$$B. 27$$
$$C. 33$$
$$D. 36$$
$$E. 48$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Joined: 31 Oct 2013 Posts: 1491 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: How many multiples of 33 lie between 101 and 1,000, inclusive? [#permalink] ### Show Tags 20 Sep 2018, 01:13 2 2 MathRevolution wrote: [Math Revolution GMAT math practice question] How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive? $$A. 24$$ $$B. 27$$ $$C. 33$$ $$D. 36$$ $$E. 48$$ First multiple of 33 in the range : 132 (33*4) Last Multiple in the range : 990 (33*30) No. of multiple in the range : (30-4) + 1 = 27. The best answer is B. GMAT Club Legend Joined: 11 Sep 2015 Posts: 4542 Location: Canada GMAT 1: 770 Q49 V46 Re: How many multiples of 33 lie between 101 and 1,000, inclusive? [#permalink] ### Show Tags 20 Sep 2018, 05:19 Top Contributor 2 MathRevolution wrote: [Math Revolution GMAT math practice question] How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive? $$A. 24$$ $$B. 27$$ $$C. 33$$ $$D. 36$$ $$E. 48$$ Some positive multiples of 33 are: 33, 66, 99, 132, 165, 198,. . . , 957, 990, 1023 So, we want the number of multiples of 33 from 132 to 990 inclusive Observe: 132 = (33)(4) 165 = (33)(5) 198 = (33)(6) . . . 957 = (33)(29) 990 = (33)(30) We can see that the number of multiples of 33 from 132 to 990 inclusive is the SAME as the number of integers from 4 to 30 inclusive. To determine the above, we can apply the following rule: the number of integers from x to y inclusive equals y - x + 1 So, the number of integers from 4 to 30 inclusive = 30 - 4 + 1 = 27 Answer: B Cheers, Brent _________________ Test confidently with gmatprepnow.com GMAT Club Legend Joined: 11 Sep 2015 Posts: 4542 Location: Canada GMAT 1: 770 Q49 V46 Re: How many multiples of 33 lie between 101 and 1,000, inclusive? [#permalink] ### Show Tags 20 Sep 2018, 05:23 Top Contributor 2 MathRevolution wrote: [Math Revolution GMAT math practice question] How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive? $$A. 24$$ $$B. 27$$ $$C. 33$$ $$D. 36$$ $$E. 48$$ Another approach is to apply the following rule: If x and y are multiples of k, then the number of multiples of k from x to y inclusive = [(y-x)/k] + 1 So, for example, the multiples of 3 from 6 to 21 inclusive = [(21 - 6)/3] + 1 = [15/3] + 1 = 6 So, the number of multiples of 33 from 132 to 990 inclusive = (990 - 132)/33 + 1 = 858/33 + 1 = 26 + 1 = 27 Answer: B Cheers, Brent _________________ Test confidently with gmatprepnow.com Director Joined: 04 Aug 2010 Posts: 546 Schools: Dartmouth College Re: How many multiples of 33 lie between 101 and 1,000, inclusive? [#permalink] ### Show Tags 20 Sep 2018, 05:34 MathRevolution wrote: [Math Revolution GMAT math practice question] How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive? $$A. 24$$ $$B. 27$$ $$C. 33$$ $$D. 36$$ $$E. 48$$ Since 1000 - 101 ≈ 900 -- and the answer choices are a bit spread out -- we can count the multiples of 33 simply by dividing 33 into 900: 900/33 = 300/11 = a bit more than 27. Thus, there are 27 multiples of 33 between 101 and 1000. _________________ GMAT and GRE Tutor New York, NY Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 936 How many multiples of 33 lie between 101 and 1,000, inclusive? [#permalink] ### Show Tags 20 Sep 2018, 07:07 MathRevolution wrote: [Math Revolution GMAT math practice question] How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive? $$A. 24$$ $$B. 27$$ $$C. 33$$ $$D. 36$$ $$E. 48$$ One of our students´ most-loved mottos is: let the "Queen of Sciences" (Mathematics) do the weight-lifting for you! $$101 < 33M < 1000$$ $$? = M\,\,\,\left( {\operatorname{int} } \right)$$ $$\left( {99 + 33 = } \right)\,\,\,132 \leqslant 33M \leqslant 990\,\,\,\,\left( { = 30 \cdot 33} \right)$$ $$4 \leqslant M \leqslant 30\,\,\,\, \Rightarrow \,\,\,\,? = 30 - 4 + 1 = 27$$ This solution follows the notations and rationale taught in the GMATH method. Regards, fskilnik. P.S.: that´s EXACTLY Selim´s solution, only a bit more "structured". Congrats, Selim!! _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8722 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: How many multiples of 33 lie between 101 and 1,000, inclusive? [#permalink] ### Show Tags 24 Sep 2018, 05:12 => Consider the arithmetic sequence $$132, 165, …, 990$$ of multiples of $$33$$. The number of terms in this sequence is $$\frac{(990-132)}{33} + 1 =\frac{858}{33} + 1 = 26 + 1 = 27.$$ 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$79 for 1 month Online Course"
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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?  [#permalink]

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08 Feb 2020, 19:49
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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?   [#permalink] 08 Feb 2020, 19:49
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