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If 3 < x < 100, for how many values of x is x/3 the square o
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07 Aug 2020, 10:02
07 Aug 2020, 10:02
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Question Stats:
74% (01:46) correct
24% (01:51) wrong based on 28 sessions
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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
Kudos for the right solution and explanation
(A) Two
(B) Three
(C) Four
(D) Five
(E) Nine
Kudos for the right solution and explanation
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 3 < x < 100, for how many values of x is x/3 the square o
[#permalink]
07 Aug 2020, 10:20
07 Aug 2020, 10:20
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Carcass 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
Kudos for the right solution and explanation
(A) Two
(B) Three
(C) Four
(D) Five
(E) Nine
Kudos for the right solution and explanation
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: B
Re: If 3 < x < 100, for how many values of x is x/3 the square o
[#permalink]
09 Aug 2020, 09:56
09 Aug 2020, 09:56
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x/3 = p^2 where p is a prime number
therefore
x=3p^2
and we need 3<x<100
We start listing prime numbers
2, 3, 5, 7, 11
We square them
4, 9, 25, 49, 121
We times them by 3
12, 27, 75, 147,...
only 12, 27, 75 are between 3 and 100
Final Answer: B
therefore
x=3p^2
and we need 3<x<100
We start listing prime numbers
2, 3, 5, 7, 11
We square them
4, 9, 25, 49, 121
We times them by 3
12, 27, 75, 147,...
only 12, 27, 75 are between 3 and 100
Final Answer: B
