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Math Expert V
Joined: 02 Sep 2009
Posts: 59068
If v = (w)^2(y)(z), how many positive factors does v have?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 75% (01:02) correct 25% (01:13) wrong based on 131 sessions

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If v = (w)^2(y)(z), how many positive factors does v have?

(1) w, y and z are integers greater than 1
(2) w, y and z are distinct prime numbers

_________________
Manager  B
Joined: 07 May 2015
Posts: 174
Location: India
GMAT 1: 660 Q48 V31 GPA: 3
Re: If v = (w)^2(y)(z), how many positive factors does v have?  [#permalink]

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St 1 insufficient
St2: w y and z are prime so number of factors is ;
(2+1)(1+1)(1+1) = 12
Sufficient

Ans: B
Current Student D
Joined: 12 Aug 2015
Posts: 2549
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If v = (w)^2(y)(z), how many positive factors does v have?  [#permalink]

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Here B is clearly sufficient as we know we really dont have to know the prime factors actually => knowing there powers is enough to get the fators
Hence B
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Senior Manager  Joined: 20 Aug 2015
Posts: 384
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GMAT 1: 760 Q50 V44 Re: If v = (w)^2(y)(z), how many positive factors does v have?  [#permalink]

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Bunuel wrote:
If v = (w)^2(y)(z), how many positive factors does v have?

(1) w, y and z are integers greater than 1
(2) w, y and z are distinct prime numbers

Given: v = (w)^2(y)(z)
Required: Number of positive factors of v

We can find the number of factors of N = (x^a)*(y^b)*(z^c) if x, y and z are different prime numbers.
Number of factors = (a+1)(b+ 1)(c+1)

Statement 1: w, y and z are integers greater than 1
If w,y and z are prime, we can find the number of factors. If they are not, we cannot find.
INSUFFICIENT

Statement 2: w, y and z are distinct prime numbers
This clearly tells us that w,y and z are distinct prime numbers.
Hence we can find the number of factors.
Number of factors = 3*2*2 = 12 (Not needed to calculate for the question)
SUFFICIENT

Option B
Intern  B
Joined: 22 May 2017
Posts: 5
If v = (w)^2(y)(z), how many positive factors does v have?  [#permalink]

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TeamGMATIFY wrote:
Bunuel wrote:
If v = (w)^2(y)(z), how many positive factors does v have?

(1) w, y and z are integers greater than 1
(2) w, y and z are distinct prime numbers

Given: v = (w)^2(y)(z)
Required: Number of positive factors of v

We can find the number of factors of N = (x^a)*(y^b)*(z^c) if x, y and z are different prime numbers.
Number of factors = (a+1)(b+ 1)(c+1)

Statement 1: w, y and z are integers greater than 1
If w,y and z are prime, we can find the number of factors. If they are not, we cannot find.
INSUFFICIENT

Statement 2: w, y and z are distinct prime numbers
This clearly tells us that w,y and z are distinct prime numbers.
Hence we can find the number of factors.
Number of factors = 3*2*2 = 12 (Not needed to calculate for the question)
SUFFICIENT

Option B

What if W is negative?
Statement 2 doesnot bound for any of the prime factors to be negative?
If they would have asked for the factors the above explanation is fine.
but they have specifically asked for positive and then both the possibilities must be considered.
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1417
Location: India
Re: If v = (w)^2(y)(z), how many positive factors does v have?  [#permalink]

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akgulhane wrote:
TeamGMATIFY wrote:
Bunuel wrote:
If v = (w)^2(y)(z), how many positive factors does v have?

(1) w, y and z are integers greater than 1
(2) w, y and z are distinct prime numbers

Given: v = (w)^2(y)(z)
Required: Number of positive factors of v

We can find the number of factors of N = (x^a)*(y^b)*(z^c) if x, y and z are different prime numbers.
Number of factors = (a+1)(b+ 1)(c+1)

Statement 1: w, y and z are integers greater than 1
If w,y and z are prime, we can find the number of factors. If they are not, we cannot find.
INSUFFICIENT

Statement 2: w, y and z are distinct prime numbers
This clearly tells us that w,y and z are distinct prime numbers.
Hence we can find the number of factors.
Number of factors = 3*2*2 = 12 (Not needed to calculate for the question)
SUFFICIENT

Option B

What if W is negative?
Statement 2 doesnot bound for any of the prime factors to be negative?
If they would have asked for the factors the above explanation is fine.
but they have specifically asked for positive and then both the possibilities must be considered.

Hello

The statement says: "w, y, z are distinct prime numbers". Prime numbers cannot be negative. They are only positive.
So 2, 3 are prime but -2 and -3 are not prime. Re: If v = (w)^2(y)(z), how many positive factors does v have?   [#permalink] 23 Mar 2018, 05:00
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