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If p is an integer such that 20 < p < 40 and p has exactly three posit

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carcass
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If p is an integer such that 20 < p < 40 and p has exactly three posit [#permalink] New post   05 Sep 2022, 05:28
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If p is an integer such that 20 < p < 40 and p has exactly three positive factors, what is the value of √p?

(A) 3
(B) 5
(C) 6
(D) 3√2
(E) 4√2


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Re: If p is an integer such that 20 < p < 40 and p has exactly three posit [#permalink] New post   05 Sep 2022, 09:29
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a square of a prime number has three +ve factors
for given range 20<p<40
p has to be 25
so√25 ; 5
option B

carcass wrote:
If p is an integer such that 20 < p < 40 and p has exactly three positive factors, what is the value of √p?

(A) 3
(B) 5
(C) 6
(D) 3√2
(E) 4√2


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Re: If p is an integer such that 20 < p < 40 and p has exactly three posit [#permalink] New post   05 Sep 2022, 09:39
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carcass wrote:
If p is an integer such that 20 < p < 40 and p has exactly three positive factors, what is the value of √p?

(A) 3
(B) 5
(C) 6
(D) 3√2
(E) 4√2


If a number has an ODD NUMBER OF FACTORS, then that number is a perfect square
In the range mentioned above, only two numbers are perfect squares - 25 and 36
Out of these numbers, only 25 has only three positive factors

So sqrt(25) = 5

Answer - B
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Re: If p is an integer such that 20 < p < 40 and p has exactly three posit [#permalink] New post   26 Sep 2023, 05:58
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carcass wrote:
If p is an integer such that 20 < p < 40 and p has exactly three positive factors, what is the value of √p?

(A) 3
(B) 5
(C) 6
(D) 3√2
(E) 4√2



What does ONLY three factors mean?
Any number will have at least two factors 1 and the number itself. => 1*n=n
Only way to have just one more factor, say z, is when z*z=n
Thus, three factors mean the number is a perfect square of a prime number. Factors=1, z and z^2

Now the number or perfect square is between 20 and 40. Two such numbers 25 and 36, but 36 is not a perfect square of prime number.

Answer is \(5^2=25\)


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Re: If p is an integer such that 20 < p < 40 and p has exactly three posit [#permalink]
26 Sep 2023, 05:58
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