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# What is the value of x? (1) x has exactly 3 factors. (2) 10 < x < 45

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What is the value of x? (1) x has exactly 3 factors. (2) 10 < x < 45  [#permalink]

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15 Sep 2015, 00:18
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45% (medium)

Question Stats:

57% (01:13) correct 43% (01:09) wrong based on 242 sessions

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What is the value of x?

(1) x has exactly 3 factors.
(2) 10 < x < 45

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Math Expert
Joined: 02 Sep 2009
Posts: 56275
Re: What is the value of x? (1) x has exactly 3 factors. (2) 10 < x < 45  [#permalink]

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15 Sep 2015, 02:15
1
What is the value of x?

(1) x has exactly 3 factors.
(2) 10 < x < 45

HINT:
1. What kind of integers have odd number of factors?
2. What kind of integers have 3 factors?
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Re: What is the value of x? (1) x has exactly 3 factors. (2) 10 < x < 45  [#permalink]

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15 Sep 2015, 02:19
1
What is the value of x?

(1) x has exactly 3 factors.
(2) 10 < x < 45

(1) x has exactly 3 factors. Insufficient. We have can 3^2,5^2 and so on.
(2) 10 < x < 45. Clearly Insufficient

Using both statements, only one solution is possible i.e 5^2=25
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Re: What is the value of x? (1) x has exactly 3 factors. (2) 10 < x < 45  [#permalink]

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15 Sep 2015, 03:10
4
Bunuel wrote:
What is the value of x?

(1) x has exactly 3 factors.
(2) 10 < x < 45

HINT:
1. What kind of integers have odd number of factors?
2. What kind of integers have 3 factors?

1. Integers, whose square root are also integers, have odd number of factors.
2. square of prime has exactly 3 factors.
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Re: What is the value of x? (1) x has exactly 3 factors. (2) 10 < x < 45  [#permalink]

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15 Sep 2015, 03:14
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3
nahid78 wrote:
Bunuel wrote:
What is the value of x?

(1) x has exactly 3 factors.
(2) 10 < x < 45

HINT:
1. What kind of integers have odd number of factors?
2. What kind of integers have 3 factors?

1. Integers, whose square root are also integers, have odd number of factors.
2. square of prime has exactly 3 factors.

That's correct.

1. Positive perfect squares have odd number of factors: 1, 4, 9, 16, 25, ...
2. Only the squares of primes have 3 factors: 4, 9, 25, 49, ...
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Re: What is the value of x? (1) x has exactly 3 factors. (2) 10 < x < 45  [#permalink]

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25 Jul 2017, 16:14
What is the value of x?

(1) x has exactly 3 factors.
(2) 10 < x < 45

We can just apply a simple rule- the square of a prime has only 3 factors.

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Re: What is the value of x? (1) x has exactly 3 factors. (2) 10 < x < 45  [#permalink]

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31 Jan 2019, 05:04
1
Bunuel wrote:
What is the value of x?

(1) x has exactly 3 factors.
(2) 10 < x < 45

HINT:
1. What kind of integers have odd number of factors?
2. What kind of integers have 3 factors?

Hi Bunuel,

We have 3 values between 10 and 45 which are perfect squares (16,25,36), So we have three values for X. Shouldn't the answer be E?
Re: What is the value of x? (1) x has exactly 3 factors. (2) 10 < x < 45   [#permalink] 31 Jan 2019, 05:04
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