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# How many numbers between 1 and 200, inclusive, have a 2 in the units

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8007
GMAT 1: 760 Q51 V42
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How many numbers between 1 and 200, inclusive, have a 2 in the units  [#permalink]

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11 Feb 2019, 02:44
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Difficulty:

45% (medium)

Question Stats:

75% (01:44) correct 25% (02:14) wrong based on 57 sessions

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[GMAT math practice question]

How many numbers between $$1$$ and $$200$$, inclusive, have a $$2$$ in the units place and are divisible by $$4$$?

A. 8
B. 9
C. 10
D. 11
E. 12

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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" Math Expert Joined: 02 Aug 2009 Posts: 7960 Re: How many numbers between 1 and 200, inclusive, have a 2 in the units [#permalink] ### Show Tags 11 Feb 2019, 04:21 MathRevolution wrote: [GMAT math practice question] How many numbers between $$1$$ and $$200$$, inclusive, have a $$2$$ in the units place and are divisible by $$4$$? $$A. 8$$ $$B. 9$$ $$C. 10$$ $$[m]D. 11$$ E. 12[/m] Hi... The property of divisibility by 4 is that the last two digits are divisible by 4.. Now if the number is x2, x has to be an odd number for being divisible by 4, so x can take any of 5 odd numbers. Alsi the hundreds digit could be 0 or 1 that is 0x2 or 1x2, so 2 ways Total 2*5=10 C OA is wrong as A is not the answer _________________ Manager Joined: 14 May 2018 Posts: 96 Location: India Concentration: Finance, Entrepreneurship GMAT 1: 710 Q49 V38 GPA: 4 Re: How many numbers between 1 and 200, inclusive, have a 2 in the units [#permalink] ### Show Tags 11 Feb 2019, 04:53 MathRevolution wrote: [GMAT math practice question] How many numbers between $$1$$ and $$200$$, inclusive, have a $$2$$ in the units place and are divisible by $$4$$? $$A. 8$$ $$B. 9$$ $$C. 10$$ $$[m]D. 11$$ E. 12[/m] Just see the series 12,32,52...192 There will be 10 numbers Ans:C _________________ Please hit kudos if you like my answers. GMAT:710 (Q49,V38,IR8,AWA5) Manager Joined: 19 Jan 2019 Posts: 88 Re: How many numbers between 1 and 200, inclusive, have a 2 in the units [#permalink] ### Show Tags 11 Feb 2019, 06:38 How is A the right answer... From 1 to 100 there are 5 multiples of 4 which have 2 in its units place ( 12,32,52,72,92). The same repeats in 100-200 ( 112,132,152,172,192) Therefore there are 10 such numbers.... Option c must be the right answer. Posted from my mobile device GMAT Club Legend Joined: 18 Aug 2017 Posts: 4999 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: How many numbers between 1 and 200, inclusive, have a 2 in the units [#permalink] ### Show Tags Updated on: 12 Feb 2019, 05:43 MathRevolution wrote: [GMAT math practice question] How many numbers between $$1$$ and $$200$$, inclusive, have a $$2$$ in the units place and are divisible by $$4$$? $$A. 8$$ $$B. 9$$ $$C. 10$$ $$[m]D. 11$$ E. 12[/m] total integers divisible by 4 from 1 to 200 = 50 and unit digit of 2 would come when 4 is multiplied by 3 or 8 so we can have two set of digit ranges ( 3,13,23,33,43) and ( 8,18,28,38,48) total = 10 IMO C Originally posted by Archit3110 on 12 Feb 2019, 05:32. Last edited by Archit3110 on 12 Feb 2019, 05:43, edited 1 time in total. Director Joined: 09 Mar 2018 Posts: 996 Location: India Re: How many numbers between 1 and 200, inclusive, have a 2 in the units [#permalink] ### Show Tags 12 Feb 2019, 05:42 MathRevolution wrote: [GMAT math practice question] How many numbers between $$1$$ and $$200$$, inclusive, have a $$2$$ in the units place and are divisible by $$4$$? $$A. 8$$ $$B. 9$$ $$C. 10$$ $$[m]D. 11$$ E. 12[/m] There will be a difference of 20 among the cases which have a $$2$$ in the units place and are divisible by $$4$$ 12 ,32,52,72,92,112,132,152,172,192 C _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8007 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: How many numbers between 1 and 200, inclusive, have a 2 in the units [#permalink] ### Show Tags 13 Feb 2019, 01:54 => In order for a number with 2 in the units place to be divisible by 4, the last two digits must be one of 12, 32, 52, 72 and 92. Thus, the numbers between 1 and 200, inclusive, satisfying this property are 12, 32, 52, 72, 92, 112, 132, 152 and 172. There are 8 such numbers. Therefore, A is the answer. 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$79 for 1 month Online Course"
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Re: How many numbers between 1 and 200, inclusive, have a 2 in the units   [#permalink] 13 Feb 2019, 01:54
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