If k is an integer and 121

Question

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

A. 3
B. 4
C. 5
D. 6
E. 8

shreyast · Answer

Since  k^2  is between, 121 =  11^2  and 225 =  15^2 , k can be 12, 13, 14, -12, -13 and -14.
Note that 11 and 15 cannot be included since the question doesn't mention equality.

Lucky2783 · Answer

given k is an integer 
121 < k^2 < 225

11 < | k| < 15

K=-12,-13,-14,12,13,14

D is the Answer .

mehtakaustubh · Answer

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

AVRonaldo · Answer

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)

KS15 · Answer

Answer=D

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

Turkish · Answer

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

EMPOWERgmatRichC · Answer

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

OptimusPrepJanielle · Answer

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

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: findkgivenrangeforksquared_text.PNG 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.

PareshGmat · Answer

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

144 = (\pm12)^2

169 = (\pm13)^2

196 = (\pm14)^2

Total possible values = 6

Answer = D

Abhishek009 · Answer

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

bumpbot · Answer

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

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