Hi beatgmatny1,

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

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

beatgmatny1 wrote:Hello,

How many ODD numbers between 10 and 1000 are the squares of the integers?

A) 12
B) 13
C) 14
D) 15
E) 16

First notice (ODD number)² = ODD number
And (EVEN number)² = 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 5² = 25)
The next integer is 49 (since 7² = 49)
The next integer is 81 (since 9² = 81)
.
.
.

IMPORTANT: Now let's find the largest odd integer (that's less than 1000) that works.
900 is a good starting point, because 30² = 900
31² = 961
At this point, I know that 32² will likely evaluate to be an integer greater than 1000, and even if it isn't greater than 1000, 33² will DEFINITELY be greater than 1000

So, we get:
25 (since 5² = 25)
49 (since 7² = 49)
81 (since 9² = 81)
.
.
.
961 (since 31² = 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