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If 3 < x < 100, for how many values of x is x/3 the square

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If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 13 Dec 2012, 08:35
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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
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 13 Dec 2012, 08:39
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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.
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 13 Dec 2012, 08:48
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x/3 is a square or we can take x/3 as y^2; x = y^2 * 3.
Since x should be between 3 and 100, y^2 can take squares 4, 9 and 25.
Answer B.
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 19 Dec 2012, 06:19
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For x/3 to be a square of a prime number, x = (prime no)^2 x 3

List squares of some prime nos:
4,9,25,49

x can be:

4x3, 9x3 and 25x3

Anything above 25x3 will make x>100, but we are given that 3<x<100

Hence, 3 nos, Option B.
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 19 Dec 2012, 06:26
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] New post 08 Jul 2013, 02:58
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 got confused in this question...why are we considering values 2 and 3 when it is given that 3<x<100...
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 08 Jul 2013, 03:31
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anu1984 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



I got confused in this question...why are we considering values 2 and 3 when it is given that 3<x<100...


The question is: for how many values of x is x/3 the square of a prime number.

The answer is: for three values of x (namely for 12, 27, and 75) x/3 is the square of a prime number.

Hope it's clear.
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 08 Jul 2013, 04:12
Bunuel wrote:
anu1984 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



I got confused in this question...why are we considering values 2 and 3 when it is given that 3<x<100...


The question is: for how many values of x is x/3 the square of a prime number.

The answer is: for three values of x (namely for 12, 27, and 75) x/3 is the square of a prime number.

Hope it's clear.


Yes got it now...thanks..
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 05 Apr 2014, 14:40
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?
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 05 Apr 2014, 15:18
Expert's post
russ9 wrote:
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?


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.
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 07 Apr 2014, 00:18
Setting up the equation as follows:

\frac{x}{3} should be a square

So, say \frac{x}{3} = a^2

x = 3a^2

3 < 3 a^2 < 100

For a = 1; the condition fails

For a = 2; x = 12

For a = 3; x = 27

For a = 5; x = 75

For a = 7; condition fails

Answer = 3 = B
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 09 May 2014, 14:40
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.


Hi Bunuel,

Can you perhaps recommend a few similar problems?

Thanks!
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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 10 May 2014, 04:18
Expert's post
russ9 wrote:
Bunuel wrote:
russ9 wrote:

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.


Hi Bunuel,

Can you perhaps recommend a few similar problems?

Thanks!


Check this one: for-how-many-values-of-k-is-12-12-the-least-common-multiple-86737.html
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If 3 < x < 100, for how many values of x is x/3 the square [#permalink] New post 12 Sep 2014, 05:12
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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



x/3 the square of a prime number ; 3 < x < 100..

divide the above by 3 then 1 < x/3 < 33..

so x/3 could be 4, 9, 16 25 .. since 16 is a square of 4 , which is not a prime answer should be 3.
Re: If 3 < x < 100, for how many values of x is x/3 the square   [#permalink] 12 Sep 2014, 05:12
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