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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink]

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19 Dec 2012, 07:26

Walkabout wrote:

If 3 < x < 100, for how many values of x is x/3 the square of a prime number?

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

I think Bunnuel has given a perfect explanation that needs no further detailing.

I just want to highlight a point in these types of questions. For the questions that ask "how many values of x".. they will usually be of consecutive numbers. But when the numbers asked are primes, then it is manual counting that is required because prime numbers do not follow any standard pattern. They will definitely be countable and the total will usually be less than 25 in GMAT.
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink]

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05 Apr 2014, 15:40

Bunuel wrote:

Walkabout wrote:

If 3 < x < 100, for how many values of x is x/3 the square of a prime number?

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

Since \(3 < x < 100\), then \(1<\frac{x}{3}<33\frac{1}{3}\) (just divide all parts of the inequality by 3).

\(\frac{x}{3}\) should be the square of a prime number, thus \(\frac{x}{3}\) could be 2^2=4, 3^2=9, or 5^2=25.

Answer: B.

Going through the explanation, I get *why* the answer is 3 but unfortunately, I wouldn't have been able to come to that solution on my own.

If I treat this problem as substitution, i can sub x=Prime^2 * 3 and then solve but why did you take the other route? Why did you divide both sides of the inequality by 3?

If 3 < x < 100, for how many values of x is x/3 the square of a prime number?

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

Since \(3 < x < 100\), then \(1<\frac{x}{3}<33\frac{1}{3}\) (just divide all parts of the inequality by 3).

\(\frac{x}{3}\) should be the square of a prime number, thus \(\frac{x}{3}\) could be 2^2=4, 3^2=9, or 5^2=25.

Answer: B.

Going through the explanation, I get *why* the answer is 3 but unfortunately, I wouldn't have been able to come to that solution on my own.

If I treat this problem as substitution, i can sub x=Prime^2 * 3 and then solve but why did you take the other route? Why did you divide both sides of the inequality by 3?

You should use whichever approach suits you the best and gives the correct answer in minimum time.

As for my solution, I divided by 3 because this way I directly get the range for x/3 (\(1<\frac{x}{3}<33\frac{1}{3}\)), and it becomes easier to evaluate the number of values for it.
_________________

Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink]

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09 May 2014, 15:40

Bunuel wrote:

russ9 wrote:

Bunuel wrote:

Going through the explanation, I get *why* the answer is 3 but unfortunately, I wouldn't have been able to come to that solution on my own.

If I treat this problem as substitution, i can sub x=Prime^2 * 3 and then solve but why did you take the other route? Why did you divide both sides of the inequality by 3?

You should use whichever approach suits you the best and gives the correct answer in minimum time.

As for my solution, I divided by 3 because this way I directly get the range for x/3 (\(1<\frac{x}{3}<33\frac{1}{3}\)), and it becomes easier to evaluate the number of values for it.

You should use whichever approach suits you the best and gives the correct answer in minimum time.

As for my solution, I divided by 3 because this way I directly get the range for x/3 (\(1<\frac{x}{3}<33\frac{1}{3}\)), and it becomes easier to evaluate the number of values for it.

Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink]

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15 Jun 2015, 18:29

I got B

x/3 = (prime)^2 x = 3(prime) ^2

The only values for x that are 3 < x < 100 are if the prime numbers are 2,3 and 5. Once you hit 7 your x value becomes greater than 100. Therefore there are only 3 values for x.

If 3 < x < 100, for how many values of x is the square of a prime number?

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

Hi nahid78,

If your question asks how many values of x, then the answer will be 5 The values would be 4, 9, 25, 49, 81

But if you have mistyped the question and we are required to find the values of (x/3) then the values would be 12, 27, 75. Three values
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