GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 07 Apr 2020, 15:20

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62619
If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

### Show Tags

20 Mar 2018, 22:26
1
4
00:00

Difficulty:

75% (hard)

Question Stats:

53% (01:58) correct 47% (02:04) wrong based on 113 sessions

### HideShow timer Statistics

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

_________________
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 720
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]

### Show Tags

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.

Best,
_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Intern
Joined: 30 Jan 2020
Posts: 4
Location: Belarus
Schools: HEC
Re: If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

### Show Tags

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,
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9972
Location: United States (CA)
Re: If n is an integer such that 15 < n < 250, for how many possible value  [#permalink]

### Show Tags

09 Feb 2020, 04:23
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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

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
Display posts from previous: Sort by