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What is the value of the integer z ?

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What is the value of the integer z ?  [#permalink]

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New post 02 Aug 2017, 10:54
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59% (01:03) correct 41% (01:07) wrong based on 34 sessions

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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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What is the value of the integer z ?  [#permalink]

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New post Updated on: 02 Aug 2017, 11:40
sananoor wrote:
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.


Error in my solution for statement 2. Anyone looking for a solution, look for the solution right below my post. It corrects my oversight!

1) z = \(p^a\) where p is prime.
z = 2 or \(2^2\) or 3 or some other prime factor.
Insufficient.

2) 18 < z < 32
z = 2*3*5 = 30
Sufficient.

B is the answer.
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Originally posted by akshayk on 02 Aug 2017, 10:59.
Last edited by akshayk on 02 Aug 2017, 11:40, edited 1 time in total.
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What is the value of the integer z ?  [#permalink]

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New post 02 Aug 2017, 11:29
sananoor wrote:
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) All the prime numbers have exactly one prime factor. NOT SUFFICIENT

2) Only a square of prime number(say x^2) can have exactly 3 prime factors. They will be 1,x and x^2.
Between 18 and 32, only number which satisfies this is 25(5^2). SUFFICIENT

Hence B

30 has the following factors
1,2,3,5,6,10,15,30
(Note that option 2 doesn't state that the three factors are prime factors.)
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Re: What is the value of the integer z ?  [#permalink]

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New post 02 Aug 2017, 11:32
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akshayk wrote:
sananoor wrote:
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) z = \(p^a\) where p is prime.
z = 2 or \(2^2\) or 3 or some other prime factor.
Insufficient.

2) 18 < z < 32
z = 2*3*5 = 30
Sufficient.

B is the answer.


Option 2 doesn't mention that the three factors are prime factors. so only 25 satisfies the condition.
Also factors of 30 include 1,2,3,5,6,10,15,30.
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Re: What is the value of the integer z ?  [#permalink]

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New post 02 Aug 2017, 11:37
Thanks for pointing out my oversight mate!

Posted from my mobile device

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Re: What is the value of the integer z ? &nbs [#permalink] 02 Aug 2017, 11:37
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