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Difficulty:
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37%
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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.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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Updated on: 31 Jan 2020, 04:04
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.
Last edited by GMATinsight on 31 Jan 2020, 04:04, edited 4 times in total.
Quote:
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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CareerGeek
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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
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
GMAT 1: 720 Q49 V40
Posts: 939
(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)
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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GMAT 3: 720 Q50 V38
Posts: 816
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
(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
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.
Posted from my mobile device
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.
Posted from my mobile device
Archit3110
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Status:You learn more from failure than from success.
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GPA: 4
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GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,815
#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.
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.
Posts: 14
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
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
ostrick5465
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Last visit: 24 Jul 2026
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Location: Viet Nam
WE:Education (Education)
Products:
Posts: 196
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
_________________
(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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My Goal: GMAT 740+
From stmnt (1), Z has many values. Not Sufficient.
From stmnt (2), 25 has only 3 factor .( B)
From stmnt (2), 25 has only 3 factor .( B)
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
Posted from my mobile device
(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
Posted from my mobile device
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