Author 
Message 
TAGS:

Hide Tags

Stern Thread Master
Joined: 26 Jul 2014
Posts: 65

How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
27 Jul 2014, 16:17
Question Stats:
67% (02:00) correct 33% (02:12) wrong based on 457 sessions
HideShow timer Statistics
How many odd numbers between 10 and 1,000 are the squares of integers? A. 12 B. 13 C. 14 D. 15 E. 16
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59561

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
27 Jul 2014, 16:25
eleuth wrote: How many odd numbers between 10 and 1,000 are the squares of integers?
A. 12 B. 13 C. 14 D. 15 E. 16 The square of an odd number is an odd number: 10 < odd < 1,000 10 < odd^2 < 1,000 3.something < odd < 31.something (by taking the square root). So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31. 14 numbers. Answer: C.




Intern
Joined: 05 Apr 2013
Posts: 7
Concentration: Operations, Finance
GPA: 3.8

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
11 Nov 2014, 22:27
We know that only squares of odd numbers are odd 1^2=1, 3^2=9, 5^2=25........31^2=961,33^2=1089 we can see that squares of numbers between 5 and 31, inclusive, are the odd numbers lying between 10 and 1000 to find out how many numbers lie between 5 and 31, we may use sequences formula nth term=first term + (no of terms  1)*common difference we have 31=5+(n1)*2 Solving we get n=14 Hence Answer is choice (C)



Intern
Joined: 05 Aug 2014
Posts: 27

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
28 Jul 2015, 03:49
Bunuel wrote: eleuth wrote: How many odd numbers between 10 and 1,000 are the squares of integers?
A. 12 B. 13 C. 14 D. 15 E. 16 The square of an odd number is an odd number: 10 < odd < 1,000 10 < odd^2 < 1,000 3.something < odd < 31.something (by taking the square root). So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31. 14 numbers. Answer: C. Could you please advice on how to promptly figure out the upper and lower numbers for the set of odd number squares between 10 and 1000? Generally, how do you go about these types of questions?



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
28 Jul 2015, 08:15
jadon wrote: How many odd numbers between 10 and 1,000 are the squares of integers?
A. 12 B. 13 C. 14 D. 15 E. 16 Total Perfect Squares from 1 through 1000 = 1^2 to 31^2 i.e. 31 Perfect Squares (with 15 even and 16 odd perfect squares) Odd Perfect Squares from 1 through 1000 = 31  15 = 16 perfect Squares Odd Perfect Squares from 1 through 10 = 1^2 and 3^2 = 2 perfect Squares Total Odd Perfect Squares from 10 though 1000 = 16  2 = 14 Answer: option C
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15636
Location: United States (CA)

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
28 Jul 2015, 20:38
Hi All, In these types of situations, you don't need to physically figure out every number in the set  you just have to figure out the smallest and the biggest, then you can 'count up' the number of terms in between (inclusive). Here, we're asked for ODD numbers, between 10 and 1,000, that are SQUARES of INTEGERS. Since we're looking for ODD numbers, we're looking for the SQUARES of ODD numbers.... It helps to have certain perfect squares memorized and it helps to be able to do some basic multiplication by hand... The first few perfect squares are....0, 1, 4, 9, 16, 25.... From this, we can determine the SMALLEST number that fits the above description: 25 (which is 5squared). Now we have to figure out the BIGGEST number.... Here's where having strong arithmetic skills comes in handy (we can start with 'round' numbers to 'zero in' on the BIGGEST number).... 20^2 = 400 (which is way too small) 30^2 = 900 (which is getting close to 1,000) 31^2 = 961 (which is pretty close to 1,000) 33^2 = 1,089 (which is TOO BIG). Now we know that 31squared is the largest ODD number that fits the given description....Now we just have to count up the number of terms.... The ODD numbers are... 5squared 7squared 9squared 11squared 13squared 15squared 17squared 19squared 21squared 23squared 25squared 27squared 29squared 31squared That's a total of 14 numbers. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9848
Location: Pune, India

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
28 Jul 2015, 21:26
naeln wrote: Bunuel wrote: eleuth wrote: How many odd numbers between 10 and 1,000 are the squares of integers?
A. 12 B. 13 C. 14 D. 15 E. 16 The square of an odd number is an odd number: 10 < odd < 1,000 10 < odd^2 < 1,000 3.something < odd < 31.something (by taking the square root). So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31. 14 numbers. Answer: C. Could you please advice on how to promptly figure out the upper and lower numbers for the set of odd number squares between 10 and 1000? Generally, how do you go about these types of questions? You find the closest square you can think of and then go from there. This is what I do when I want to find the first odd square after 10. I know that 9 is the square of 3. (an odd square) Next square of a number will be 4^2 which is 16 but this is an even square. So 5^2 = 25 will be the odd square closest to but greater than 10. Similarly, when I want the odd square closest to but less than 1000, I will think about 900, the square of 30 (It is very easy to see squares of numbers ending in 0 or 5). It is an even square less than 1000. The next number 31 will have an odd square. On calculating, I find that 31^2 = 961. The square of 32 is 1024 and the square of 33 will be even higher. Hence I get the range 5 to 31.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Math Expert
Joined: 02 Aug 2009
Posts: 8282

Re: How many odd numbers between 10 and 1,000 are the squares of integers?
[#permalink]
Show Tags
09 Sep 2016, 18:18
aimeehittinger wrote: How many odd numbers between 10 and 1,000 are the squares of integers? (Official question)
A. 12 B. 13 C. 14 D. 15 E. 16 We have to find the squares at the extreme ends... 10 square of 3 is 9.., so 4 is the lowest number in the series.. 1000.... clearly it is above 30^2=900.... check for 31, it is 961 and then it goes above 1000.. So we are looking for ODDs from 4 to 31... Total even and odd 314+1=28.. Odds =28/2=14 C
_________________



Intern
Joined: 12 Feb 2017
Posts: 3

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
16 Aug 2017, 12:27
Why don't we consider the negative integers here? For eg. 25 is the square of 5 and negative 5 also, so therefore in all there should be 14*2 that is 28 integers, right?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9848
Location: Pune, India

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
16 Aug 2017, 18:37
AabhishekGrover wrote: Why don't we consider the negative integers here? For eg. 25 is the square of 5 and negative 5 also, so therefore in all there should be 14*2 that is 28 integers, right? That is true but you have to count the number of perfect squares, not the number of square roots. Whether 25 is the square of one or two numbers, it doesn't matter. It is a perfect square and counted only once.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 14 Oct 2016
Posts: 5
Location: United States

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
03 Dec 2017, 11:03
I started by listing out the first few squares I knew:
1^2 = 1 2^2 = 4 3^2 = 9 4^2 = 16 5^2 = 25 6^2 = 36 7^2 = 49
At this point I realized that there was a pattern  ever other square was odd (because square of an odd is odd, and every other integer is odd).
To find upper boundary I knew 30^2 was 900 (based on 3^2 = 9 and adding two zeros for each of the 10's from each 30).
Instead of multiplying to test, I knew that 32^2 = (2^5)^2 = 2^10 = 1024, and therefore was too big. Because the difference between 1000 and 1024 is greater than 30, I assumed that the next integer down 31, was less than 1,000.
Then I counted odds between 531, to get 14.
or use ((31  5)/2) + 1 = 14
Answer C



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
12 Feb 2018, 17:42
jadon wrote: How many odd numbers between 10 and 1,000 are the squares of integers?
A. 12 B. 13 C. 14 D. 15 E. 16 The smallest odd perfect square between 10 and 1000 is 5^2 = 25. The largest odd perfect square between 10 and 1000 is 31^2 = 961. The number of odd integers from 5 to 31 inclusive is (31  5)/2 + 1 = 14. Answer: C
_________________
5star 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.



NonHuman User
Joined: 09 Sep 2013
Posts: 13709

Re: How many odd numbers between 10 and 1,000
[#permalink]
Show Tags
20 Feb 2019, 03:13
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: How many odd numbers between 10 and 1,000
[#permalink]
20 Feb 2019, 03:13






