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31 Jan 2020, 01:12
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
63% (01:37) correct
37%
(01:44)
wrong
based on 209
sessions
History
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Time
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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.
Updated on: 31 Jan 2020, 05:04
Originally posted by GMATinsight on 31 Jan 2020, 01:17.
Last edited by GMATinsight on 31 Jan 2020, 05:04, edited 4 times in total.
Last edited by GMATinsight on 31 Jan 2020, 05:04, edited 4 times in total.
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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"
31 Jan 2020, 03:03
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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
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
