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If n is an integer such that 15 < n < 250, for how many possible value

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If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

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New post 20 Mar 2018, 22:26
1
4
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A
B
C
D
E

Difficulty:

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Question Stats:

53% (02:00) correct 47% (02:01) wrong based on 118 sessions

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Re: If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

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New post 20 Mar 2018, 23:07
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Bunuel wrote:
If n is an integer such that 15 < n < 250, for how many possible values of n is n/5 the square of a prime number?

(A) Two
(B) Three
(C) Four
(D) Five
(E) Six


IMO C.

\(15 < n < 250\)
\(15/5 < n/5 < 250/5\) .... divide by 5
\(3 < n/5 < 50\)

n/5 is a perfect square for values 4 , 9 , 16, 25 , 36 & 49.

Out of which 2, 3, 5, 7 are primes of which n/5 is a square of. Hence four values.

Therefore C.

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Re: If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

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New post 05 Feb 2020, 02:10
Can someone please explain in more detail?


Gladiator59 wrote:
Bunuel wrote:
If n is an integer such that 15 < n < 250, for how many possible values of n is n/5 the square of a prime number?

(A) Two
(B) Three
(C) Four
(D) Five
(E) Six


IMO C.

\(15 < n < 250\)
\(15/5 < n/5 < 250/5\) .... divide by 5
\(3 < n/5 < 50\)

n/5 is a perfect square for values 4 , 9 , 16, 25 , 36 & 49.

Out of which 2, 3, 5, 7 are primes of which n/5 is a square of. Hence four values.

Therefore C.

Best,
Gladi
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Re: If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

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New post 09 Feb 2020, 04:23
1
Bunuel wrote:
If n is an integer such that 15 < n < 250, for how many possible values of n is n/5 the square of a prime number?

(A) Two
(B) Three
(C) Four
(D) Five
(E) Six


Letting p be a prime; we can create the equation:

n/5 = p^2

n = 5p^2

Now, we can let p = 2, 3, 5, and so on.

If p = 2, n = 5(4) = 20.

If p = 3, n = 5(9) = 45

If p = 5, n = 5(25) = 125

If p = 7, n = 5(49) = 245

We can see that if p = 11, n will be greater than 250. Therefore, there are 4 values of n such that 15 < n < 250 and n/5 is the square of a prime number.

Answer: C
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Re: If n is an integer such that 15 < n < 250, for how many possible value   [#permalink] 09 Feb 2020, 04:23

If n is an integer such that 15 < n < 250, for how many possible value

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