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# How many numbers between 1 and 1000, inclusive have an odd number of f

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42
GPA: 3.82
How many numbers between 1 and 1000, inclusive have an odd number of f  [#permalink]

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04 Apr 2019, 00:34
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Difficulty:

45% (medium)

Question Stats:

55% (01:32) correct 45% (01:49) wrong based on 33 sessions

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[GMAT math practice question]

How many numbers between 1 and 1000, inclusive have an odd number of factors?

A. 10
B. 25
C. 31
D. 64
E. 128

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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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" Director Joined: 16 Jan 2019 Posts: 507 Location: India Concentration: General Management WE: Sales (Other) How many numbers between 1 and 1000, inclusive have an odd number of f [#permalink] ### Show Tags 04 Apr 2019, 01:02 Only square numbers have an odd number of factors So the question basically asks how many squares numbers are there within 1-1000 We have 30^2=900 and therefore the answer must be a little over 30 (C) 31 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 8619 Location: United States (CA) Re: How many numbers between 1 and 1000, inclusive have an odd number of f [#permalink] ### Show Tags 07 Apr 2019, 18:28 MathRevolution wrote: [GMAT math practice question] How many numbers between 1 and 1000, inclusive have an odd number of factors? A. 10 B. 25 C. 31 D. 64 E. 128 Only perfect squares have an odd number of factors. Thus, the perfect squares between 1 and 1000, inclusive, are 1^2, 2^2, …, 31^2, so there are a total of 31 numbers. Answer: C _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8235 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: How many numbers between 1 and 1000, inclusive have an odd number of f [#permalink] ### Show Tags 07 Apr 2019, 18:41 > Recall the property that an integer with an odd number of factors is the perfect square of an integer and only has even exponents in its prime factorization. If $$n = p^aq^br^c$$, then $$n$$ has $$(a+1)(b+1)(c+1)$$ factors, where $$p, q$$ and $$r$$ are different prime numbers, and $$a, b$$ and $$c$$ are positive integers. So $$a + 1, b + 1, c + 1$$ must be odd numbers in order for $$n$$ to have an odd number of factors. This implies that $$a, b$$ and $$c$$ are even numbers and $$n$$ is the perfect square of an integer. There are $$31$$ perfect squares between $$1$$ and $$1000$$, inclusive, because $$31^2 = 961 < 1000$$ and $$32^2 = 1024 > 1000.$$ 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: How many numbers between 1 and 1000, inclusive have an odd number of f   [#permalink] 07 Apr 2019, 18:41
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