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Re: If 3 < x < 100, for how many values of x is x/3 the square
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10 May 2014, 05:18

1

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.

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

Re: If 3 < x < 100, for how many values of x is x/3 the square
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30 Aug 2017, 14:45

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1

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

We want values of x (where 3 < x < 100) such that x/3 is the square of a prime number. So, let's start checking squares of prime numbers. Some prime numbers are 2, 3, 5, 7, 11, etc

2² = 4 and (3)(4) = 12. So, x = 12 meets the given conditions. 3² = 9 and (3)(9) = 27. So, x = 27 meets the given condition 5² = 25 and (3)(25) = 75. So, x = 75 meets the given conditions. 7² = 49 and (3)(49) = 147. No good. We need values of x such that 3 < x < 100

So, there are exactly 3 values of x that meet the given conditions. Answer:

Re: If 3 < x < 100, for how many values of x is x/3 the square
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31 Oct 2017, 15:33

I did an excel spreadsheet to understand this. However, the explanation from other people to divide 100/3 = 33.33... helps to reduce the amount of work.

Re: If 3 < x < 100, for how many values of x is x/3 the square
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25 Apr 2019, 09:09

Have to read more carefully... wasted almost a minute thinking the question said the the prime number must be >3 rather than x (which would mean only 5 fits).

An easy way to do this is to revert the equation... x = prime#² * 3 Since x < 100, we can just test 2²*3 = 12 3²*3 = 27 5²*3 = 75 7²* 3 = 147, too big.