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What is the value of x?

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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Jan 20, 2019 3:43 am

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BTGmoderatorDC wrote:What is the value of x?

(1) x has exactly 3 factors.
(2) 10 < x < 45
Statement 1:
To have exactly 3 positive factors, x must be the square of a prime number.
Factors of x=2²=4:
1, 2, 4
Factors of x=3²=9:
1, 3, 9
Factors of x=5²=25:
1, 5, 25.
Since x can be different values, INSUFFICIENT.

Statement 2:
Clearly INSUFFICIENT.

Statements combined:
x must be the square of prime number such that 10 < x < 45.
Only the blue case above is viable.
Thus, x=25.
SUFFICIENT.

The correct answer is C.
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by Jay@ManhattanReview » Sun Jan 20, 2019 9:55 pm

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BTGmoderatorDC wrote:What is the value of x?

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

OA C

Source: Veritas Prep
Note that a prime number has 3 factors, a perfect square of a prime number has three factors, a perfect square of a non-prime number and others has more than three factors.

1. Prime number: Say 2, 3, 5, 7, 11. All have two factors.
2. Perfect square of prime numbers: Say 4, 9, 25, 49, etc. All have three factors.
3. Perfect square of nonprime numbers: Say 16, 36, 64, etc. All have more than three factors.
4. Others: Say 6, 8, 10, etc. All have more than three factors.

Needless to state that each statement alone is insufficient.

Only one number in the range 10 < x < 45 qualifies, i.e., x = 25.

The correct answer: C

Hope this helps!

-Jay
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