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Math Expert V
Joined: 02 Sep 2009
Posts: 62287
If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 54% (01:59) correct 46% (02:07) wrong based on 110 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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Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
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GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

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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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Intern  B
Joined: 30 Jan 2020
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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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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,
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
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Posts: 9883
Location: United States (CA)
Re: If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

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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

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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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If n is an integer such that 15 < n < 250, for how many possible value   [#permalink] 09 Feb 2020, 04:23
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