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

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Joined: 02 Sep 2009
Posts: 64125
If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

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20 Mar 2018, 22:26
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Difficulty:

75% (hard)

Question Stats:

53% (02:00) correct 47% (02:03) wrong based on 116 sessions

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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

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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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20 Mar 2018, 23:07
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

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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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.

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

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,
Re: If n is an integer such that 15 < n < 250, for how many possible value   [#permalink] 05 Feb 2020, 02:10