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What is the value of the integer z ? (1) z has exactly one prime fact
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Bunuel
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What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  31 Jan 2020, 00:12
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What is the value of the integer z ?

(1) z has exactly one prime factor.
(2) 18 < z < 32, and z has exactly three factors.
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GMATinsight
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Re: What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  Updated on: 31 Jan 2020, 04:04
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Quote:
What is the value of the integer z ?

(1) z has exactly one prime factor.
(2) 18 < z < 32, and z has exactly three factors.


Question: z = ?

Statement 1: z has exactly one prime factor.

i.e. z itself is prime or a \(Prime^{Integer}\)
i.e. z = 2, 3, 5, 7, 11,... or 2, 4, 8, 16..., 3, 9, 27, ... etc.

NOT SUFFICIENT

Statement 2: 18 < z < 32, and z has exactly three factors

i.e. Numbers in given range are {19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}

But Number with 3 factors will be of the form \(Prime^2\)

But only 25 has three factors among them because \(25 = 5^2\) whose factors are {\(1, 5, 25\)}

SUFFICIENT


ANswer: Option B


FOr property on Number of Factors please refer the following concept video made by us.


Concept on "Numbers with ODD number of factors such as 3 factos"

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Originally posted by GMATinsight on 31 Jan 2020, 00:17.
Last edited by GMATinsight on 31 Jan 2020, 04:04, edited 4 times in total.
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Dillesh4096
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Re: What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  31 Jan 2020, 02:03
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(1) z has exactly one prime factor.
Let that one prime factor of z be "\(a\)"
--> Possible values of z = {\(a\), \(a^2\), \(a^3\), . . . . . } --> Insufficient

(2) 18 < z < 32, and z has exactly three factors.
Note: A number will have 3 factors ONLY when the number if of the form \(a^2\) {Factors = 1, \(a\), \(a^2\)}
--> Possible values of z = \(5^2\) with factors {\(1\), \(5\), \(5^2\)} --> Sufficient

Option B
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Re: What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  31 Jan 2020, 02:25
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(1) z has exactly one prime factor.
z could be 2, 3, 5, 7, 4, 9, 25, 49, etc.
NOT SUFFICIENT

(2) 18 < z < 32, and z has exactly three factors.
Given such range, z must be only 25 (factors of z is 1, 5, 25)
SUFFICIENT

FINAL ANSWER IS (B)
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Re: What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  31 Jan 2020, 03:27
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What is the value of the integer z ?

(1) z has exactly one prime factor.
(2) 18 < z < 32, and z has exactly three factors.

Answer - B

Given z is an integer

1) z has exactly one prime factor -> z can me multiple values - 2, 3, 8, 9 etc -> Not sufficient

2) z has exactly 3 factors means z is a perfect square in range 18<z<32 -> Only number is 25 hence z = 25 -> Sufficient
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Re: What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  31 Jan 2020, 06:50
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We are to determine the value of z, which is an integer.

Statement 1: z has exactly one prime factor
Insufficient. This is because 4, 9, 25, etc all have exactly one prime factor and could be z.

Statement 2: 18<z<32, and z has exactly three factors.
Sufficient. We know that only the square of a prime number has exactly three factors. And the only perfect square that falls within the given range is 25, and that is the square of 5, which is a prime number. Hence z is 25.

The answer is B.

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Re: What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  31 Jan 2020, 09:54
#1
z has exactly one prime factor. ; z= 2,4,8,16 .. 5 insufficient
#2
18 < z < 32, and z has exactly three factors.
only perfect squares have three factors ; in this case 25 ; is z
IMO B sufficient

What is the value of the integer z ?

(1) z has exactly one prime factor.
(2) 18 < z < 32, and z has exactly three factors.
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Re: What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  31 Jan 2020, 21:00
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1) z has exactly one prime factor
Let "a" be the prime factor

possible - values of \( z = {a, a^2, a^3, ...}\)
Insufficient

2) \(18 < z < 32\)
and \(z \)has exactly three factors

Possible values of \(z = 5^2\) with factors \({1, 5, 5^2}\)
Sufficient

Option B
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Re: What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  02 Feb 2020, 10:38
1
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What is the value of the integer z?

(1) z has exactly one prime factor.
(2) 18 < z < 32, and z has exactly three factors.

(1) every prime number has exactly one prime factor.
in range of 18 - 32, there are many prime numbers, such as 19, 23, 29, 31
=> Not suff

(2) z has exactly three factors => z is the square of a prime number
\(3^2 = 9 \)
\(5^2 = 25 \)
\(7^2 =49\)
18< z <32 => z=25

=> Suff

=> Choice B
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Re: What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  02 Feb 2020, 11:12
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From stmnt (1), Z has many values. Not Sufficient.
From stmnt (2), 25 has only 3 factor .( B)
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Re: What is the value of the integer z ? (1) z has exactly one prime fact [#permalink] New post  02 Feb 2020, 20:24
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What is the value of the integer z ?

(Statement1): z has exactly one prime factor.
—> z could be 2,3,9,16,25....
Insufficient

(2) 18 < z < 32, and z has exactly three factors.
—> in order z to have exactly 3 factors, z must be square number.
From 18 to 32, only 25 is a square number—> z = 25
Sufficient

The answer is B

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