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# Is the positive integer z a prime number?

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Director
Joined: 12 Feb 2015
Posts: 904
Is the positive integer z a prime number?  [#permalink]

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28 Jan 2019, 08:52
3
1
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Difficulty:

65% (hard)

Question Stats:

53% (01:54) correct 47% (01:34) wrong based on 57 sessions

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Is the positive integer z a prime number?

(1) z and the square root of integer y have the same number of unique prime factors.

(2) z and the perfect square y have the same number of unique factors.

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Manish

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Intern
Joined: 24 Jan 2013
Posts: 15
GMAT 1: 660 Q49 V31
Re: Is the positive integer z a prime number?  [#permalink]

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28 Jan 2019, 10:28
2
1.
say y = 9, sqrt of y = 3 , NUMBER OF UNIQUE PRIME FACTORS =1

Now z to also have 1 number of unique prime factors , Z can be either -
3 ( PRIME )
or
9 ( NON PRIME)

Not sufficient

2.
y is a perfect square say a^2 form
Total Number of factors = 3 ( always an odd number)
For z to have same odd number of factors it can never be a prime number , because prime numbers always have only 2 factors ( 1 and number itself)
sufficient

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Director
Joined: 09 Mar 2018
Posts: 999
Location: India
Is the positive integer z a prime number?  [#permalink]

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28 Jan 2019, 09:24
CAMANISHPARMAR wrote:
Is the positive integer z a prime number?

(1) z and the square root of integer y have the same number of unique prime factors.

(2) z and the perfect square y have the same number of unique factors.

1) z and the square root of integer y have the same number of unique prime factors.

z= 3 and $$\sqrt{9}$$, will satisfy this. 3 and 3(root 9), have 1 unique factor
Will answer the question as Yes

z =14(2*7) and $$\sqrt{196}$$, will satisfy the statement. 2,7 and root 196(will give 2*7) will have 2 unique factors
Will answer the question as No

(2) z and the perfect square y have the same number of unique factors.
perfect square y can be 1,4,9,25,36,49,64

doesn't this mean they should be equal ??, only they can have same number of unique factorss

Examples 4 and 4, 8 and 16 No this wont have

z is a +ive Integer

But then z can be 1
Will answer the question as No

z can be 4
Will answer the question as No

A definite No.

IMO B
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Manager
Joined: 27 Oct 2017
Posts: 73
Re: Is the positive integer z a prime number?  [#permalink]

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08 Mar 2019, 11:36
I thought statement two is asking about the perfect square unique prime factors, so that will always be a prime number and 1, so z will be a prime number, That's why I selected B. Can someone explain?[quote][/quote]
Re: Is the positive integer z a prime number?   [#permalink] 08 Mar 2019, 11:36
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