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

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Bunuel
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If p^(1/2) is a positive integer, what is the value of p? [#permalink] New post   04 Apr 2019, 23:18
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If \(\sqrt{p}\) is a positive integer, what is the value of p?


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

(2) 11 < p < 27
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E
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Re: If p^(1/2) is a positive integer, what is the value of p? [#permalink] New post   05 Apr 2019, 00:41
Bunuel wrote:
If \(\sqrt{p}\) is a positive integer, what is the value of p?


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

(2) 11 < p < 27



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.
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Re: If p^(1/2) is a positive integer, what is the value of p? [#permalink] New post   05 Apr 2019, 01:15
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P is a perfect square.
Statement 1: 1<p^1/2<7.
P can be 4,9,16,25,36. For which root[p] 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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Re: If p^(1/2) is a positive integer, what is the value of p? [#permalink] New post   05 Apr 2019, 01:49
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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.
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If p^(1/2) is a positive integer, what is the value of p? [#permalink] New post   Updated on: 05 Apr 2019, 03:47
Bunuel wrote:
If \(\sqrt{p}\) is a positive integer, what is the value of p?


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

(2) 11 < p < 27


\(\sqrt{p}\) 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)

Originally posted by AkshdeepS on 05 Apr 2019, 01:50.
Last edited by AkshdeepS on 05 Apr 2019, 03:47, edited 2 times in total.
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Re: If p^(1/2) is a positive integer, what is the value of p? [#permalink] New post   05 Apr 2019, 03:41
Bunuel wrote:
If \(\sqrt{p}\) is a positive integer, what is the value of p?


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

(2) 11 < p < 27



#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
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Re: If p^(1/2) is a positive integer, what is the value of p? [#permalink] New post   27 Jan 2020, 23:47
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Bunuel wrote:
If \(\sqrt{p}\) is a positive integer, what is the value of p?


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

(2) 11 < p < 27


Find the solution as attached

Answer: Option E
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Screenshot 2020-01-28 at 12.17.19 PM.png
Screenshot 2020-01-28 at 12.17.19 PM.png [ 427.27 KiB | Viewed 1048 times ]

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Re: If p^(1/2) is a positive integer, what is the value of p? [#permalink]
27 Jan 2020, 23:47
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