How many odd numbers between 10 and 1,000

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

How many odd numbers between 10 and 1,000

by Vincen » Thu Feb 08, 2018 8:41 am

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 OA is the option C.

Experts, can you give me some help here? I don't know how to solve this PS question. <i class="em em-disappointed"></i>

Is there a fast way to find the correct answer? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Thu Feb 08, 2018 8:41 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Thu Feb 08, 2018 9:08 am

Vincen 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

First notice (ODD number)Â² = ODD number
And (EVEN number)Â² = EVEN number

So, we're looking for the squares of ODD integers that are between 10 and 1000

The first integer that works is 25 (since 5Â² = 25)
The next integer is 49 (since 7Â² = 49)
The next integer is 81 (since 9Â² = 81)
.
.
.

IMPORTANT: Now let's find the largest odd integer (that's less than 1000) that works.
900 is a good starting point, because 30Â² = 900
31Â² = 961
At this point, I know that 32Â² will likely evaluate to be an integer greater than 1000, and even if it isn't greater than 1000, 33Â² will DEFINITELY be greater than 1000

So, we get:
25 (since 5Â² = 25)
49 (since 7Â² = 49)
81 (since 9Â² = 81)
.
.
.
961 (since 31Â² = 961)

So, this question comes down to "How many ODD integers are there from 5 to 31 inclusive?"

At this point, we could just count them to ourselves 5, 7, 9, 11, . . . 31 to get 14

Or we can calculate [(31 - 5)/2] + 1 = 14

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Thu Feb 08, 2018 9:54 am

Hi Vincen,

You'll see some questions on the GMAT that are "just about the math." However, you might not need to do lots of math to come up with the correct answer.

Here, we're asked for the number of numbers, between 10 and 1000 that are the squares of integers. From the answers, we know that there are at least 12, but no more than 16 numbers that fit this description. Since we're given a range to work with, my though is that I should try to find the smallest and largest values, then I can just count up the number in between.

Starting at the lower end of the range, we know that....
3^2 = 9
5^2 = 25

So the smallest number is 5

Now, the upper end of the range will take a bit more work to figure out...
30^2 = 900 (we're not allowed to use even numbers though, so this calculation was just to help us "zero in" on the upper limit.
31^2 = 961 (you'll need to be comfortable doing this math by hand)

With a lower limit of 5 and an upper limit of 31, we just need to total up the ODD numbers in this range:
5 7 9
11 13 15 17 19
21 23 25 27 29
31

Total = 14

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Mon Feb 12, 2018 5:00 pm

Vincen 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

Jeffrey Miller
Head of GMAT Instruction
[email protected]