If p^(1/2) is a positive integer, what is the value of p?

Question

If  \sqrt{p}  is a positive integer, what is the value of p?

(1)  1 < \sqrt{p} < 7

(2) 11 < p < 27

KSBGC · Answer

Statement 1:  1 < \sqrt{p} < 7  . only value is 4. no other number we have in this range for which we get an integer. Sufficient.

Statement 2: 11 < p < 27 . we have 25 , 16. we can get integer if we square them. NOT sufficient.

A is the best answer.

Ypsychotic · Answer

P is a perfect square. 
Statement 1: 1<p^1/2<7.
P can be 4,9,16,25,36. For which root  lies between 1 and 7. Insufficient.
Statement 2: p is between 11 and 27. P can be 16 or 25. Insufficient.

Both
P can be 16 or 25. Insufficient. Imo, option e.

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Theblacklist · Answer

p is a perfect square. as given  \sqrt{p}  is a positive integer
Statement 1: 1< \sqrt{p} <7.
By Squaring sides
p can be 4,9,16,25,36 and  \sqrt{p}  will be 2,3,4,5,6. For which  \sqrt{p}  lies between 1 and 7. Clearly Insufficient.

Statement 2: p is between 11 and 27. p can be 16 or 25. Clearly Insufficient.

Combining both statements p can be either 16 or 25 so again insufficient.

Answer should be E.

AkshdeepS · Answer

\sqrt{p}  is a positive integer when "p" is a perfect square.

Question : What is p?

Statement 1 : 1 <  \sqrt{p}  < 7

Squaring this we get ,

1^2 < p < 7^2

1 < p < 49

Valid values of p = 4, 9, 16, 25, 36 ----- NOT SUFFICIENT

Statement 2 : 11 < p < 27

Valid values of p = 16, 25 ----- NOT SUFFICIENT

From 1 and 2 we get,

p = 16 and 25

NOT SUFFICIENT.

(E)

Archit3110 · Answer

#1
  1 < \sqrt{p} < 7 
1<p<49
p can have many values
#2
11<p<27
p can have many values
from1 & 2
nothing in common
IMO E

GMATinsight · Answer

Find the solution as attached

Answer: Option E

If p^(1/2) is a positive integer, what is the value of p?

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