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[x] is the greatest integer less than or equal to x. What is the value

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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[x] is the greatest integer less than or equal to x. What is the value  [#permalink]

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02 May 2019, 17:51
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55% (hard)

Question Stats:

67% (03:04) correct 33% (02:41) wrong based on 39 sessions

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[GMAT math practice question]

$$[x]$$ is the greatest integer less than or equal to $$x$$. What is the value of $$[√1] + [√2] + [√3] + … + [√49] + [√50]$$?

$$A. 115$$

$$B. 195$$

$$C. 217$$

$$D. 288$$

$$E. 360$$

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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" SVP Status: Top MBA Admissions Consultant Joined: 24 Jul 2011 Posts: 2029 GMAT 1: 780 Q51 V48 GRE 1: Q800 V740 Re: [x] is the greatest integer less than or equal to x. What is the value [#permalink] Show Tags 02 May 2019, 19:16 2 Top Contributor To solve this question, let us evaluate the ranges of roots till 50. For x between 1 and 3, [root(x)] will always be 1. For x between 4 and 8, it will be 2. Between 9 and 15, it will be 3. Between 16 and 24, it will be 4. Between 25 and 35, it will be 5. Between 36 and 48, it will be 6. 49 and above, it will be 7. So the sum required = 3*1 + 5*2 + 7*3 + 9*4 + 11*5 + 13*6 + 2*7 = 3 + 10 + 21 + 36 + 55 + 78 + 14 = 217. Option (C). _________________ GyanOne [www.gyanone.com]| Premium MBA and MiM Admissions Consulting Awesome Work | Honest Advise | Outstanding Results Reach Out, Lets chat! Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8792 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: [x] is the greatest integer less than or equal to x. What is the value [#permalink] Show Tags 06 May 2019, 01:37 => $$[√1] = 1$$ $$[√2] = 1$$ $$[√3] = 1$$ If $$1 ≤ n < 4$$, then $$1 ≤ √n < 2$$and $$[√n] = 1$$ for $$n = 1, 2, 3$$ ($$3$$ terms). If $$4 ≤ n < 9$$, then $$2 ≤ √n < 3$$ and $$[√n] = 2$$ for $$n = 4, 5, …, 8 (5(=8-4+1)$$ terms). If $$9 ≤ n < 16$$, then $$3 ≤ √n < 4$$ and $$[√n] = 3$$ for $$n = 9, 10, …, 15 (7$$ terms). If $$16 ≤ n < 25$$, then $$4 ≤ √n < 5$$ and $$[√n] = 4$$ for $$n = 16, 17, …, 24 (9$$ terms). If $$25 ≤ n < 36$$, then $$5 ≤ √n < 6$$ and $$[√n] = 5$$ for $$n = 25, 26, …, 35 (11$$ terms). If $$36 ≤ n < 49,$$ then $$6 ≤ √n < 7$$ and $$[√n] = 6$$ for $$n = 36, 37, …, 48 (13$$terms). If $$49 ≤ n < 64,$$ then $$7 ≤ √n < 8$$ and $$[√n] = 7$$ for $$n = 49$$ and $$50 (2$$ terms). Therefore, $$[√1] + [√2] + [√3] + … + [√49] + [√50]$$ $$= ( 1 + 1 + 1 ) + ( 2 + 2 + … + 2 ) + ( 3 + 3 + … + 3 ) + ( 4 + 4 + … + 4 ) + ( 5 + 5 + … + 5 ) + ( 6 + 6 + … + 6 ) + ( 7 + 7 )$$ $$= 1*3 + 2*5 + 3*7 + 4*9 + 5*11 + 6*13 + 7*2$$ $$= 3 + 10 + 21 + 36 + 55 + 78 + 14$$ $$= 217$$ Therefore, the answer is C. Answer: C _________________ 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: [x] is the greatest integer less than or equal to x. What is the value   [#permalink] 06 May 2019, 01:37
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