If p is an integer such that 20

Question

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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Archit3110 · Answer

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

av1901 · Answer

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

chetan2u · Answer

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

B

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

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