If k is an integer and 121 < k^2 < 225, then k can have at most how

IMO D
K^2=144,169,196
=12^2,13^2,14^2
=+12,-12,+13,-13,+14,-14

Given 121<\(k^2\)<225

Therefore, \(k^2\) is a perfect square number between 121 and 225

\(k^2\) = 144,169 and 196

Since k is an integer and \(k^2\) hides the sign of the integer , the possible values of k are -12,-13,-14,12,13, & 14

Answer is 6 (D)

Answer=D

K^12=144 OR 169 OR 196
Therefore, K=12,-12,13,-13,14,-14
K can have 6 values

Opps I forgot about the -12,-13,-14...

Hi All,

It looks like everyone has properly answered this question, so I won't rehash an explanation here. Instead, I want to point out how the GMAT will repeated test you on how well you understand certain concepts by putting those concepts into different formats. In that way, you're tested on more than just 'math knowledge', you're tested on how well you can use that knowledge under different circumstances. In this case, the concept is 'squared terms.'

For example, I bet that everyone can answer the following equation:

X^2 = 25

You should recognize that there are 2 solutions to this equation: one positive and one negative. When you start to factor in inequalities or other math concepts (absolute values, Pythagorean Theorem, etc.), you have to consider even MORE possibilities.

For example...

Z^2 < 4

Here, there is a RANGE of values (positive, negative and 0).

Part of properly training for the GMAT is to develop the proper 'reaction' to seeing certain types of information. Here, seeing K^2 should make you think "there's probably more than just a positive answer"; seeing inequalities should make you think "there's probably multiple answers."

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

We know that 121 = 11^2 and 225 = 15^2
So, 11^2 < k^2 < 15^2
So, 11 < |k| < 15
So, k = -12,12,-13,13,-14,14
Hence there are 6 possible values of k.

Hence option (D).

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

MAGOOSH OFFICIAL SOLUTION:


FAQ: How would I know to consider the negative values too?
You should always make it a point to consider negative values when you're looking for the values of a number that is being squared (^2) or is being multiplied to the 4th power (^4), etc. Basically, any even exponent (^2, ^4, ^6, ^8, etc.) means that's there's a possibility that the value of the base/your answer may be negative.

Possible values of k^2 are 144, 169, 196

\(144 = (\pm12)^2\)

\(169 = (\pm13)^2\)

\(196 = (\pm14)^2\)

Total possible values = 6

Answer = D

121 < k^2 < 225

\(= \sqrt{121} < \sqrt{k^2} < \sqrt{225}\)

\(=\) +\(11 < K <\) +\(15\)

So, We have the following values - +\(12\) , +\(13\) & +\(14\)

Thus, the correct answer must be (D) 6

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.