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If x, y, z are distinct prime numbers, which of the following could be

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Manager
Joined: 16 Jan 2018
Posts: 94
Location: New Zealand
If x, y, z are distinct prime numbers, which of the following could be  [#permalink]

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19 Aug 2018, 00:42
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Difficulty:

45% (medium)

Question Stats:

49% (00:58) correct 51% (01:07) wrong based on 85 sessions

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If x, y, z are distinct prime numbers, which of the following could be true?

I. x is the mean of the three primes.

II. xyz - 1 is a prime

III. 27 is divisible by xyz

A. Only I

B. Only II

C. Only III

D. I & II

E. I, II & II
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Joined: 11 Jun 2011
Posts: 4031
Location: India
GPA: 3.5
Re: If x, y, z are distinct prime numbers, which of the following could be  [#permalink]

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19 Aug 2018, 01:09
blueviper wrote:
If x, y, z are distinct prime numbers, which of the following could be true?

I. x is the mean of the three primes.

II. xyz - 1 is a prime

III. 27 is divisible by xyz

A. Only I

B. Only II

C. Only III

D. I & II

E. I, II & II

Plug in and check

I. Let $$x = 5, y = 3$$ and $$z = 7$$ Here mean will be $$\frac{3 + 5 + 7}{3} = 5 = x$$ (possible)

II. Let $$x = 2, y = 3$$ and $$z = 5$$ Here mean will be $$2*3*5 -1 = 29$$ (possible)

III. Definitly not possible as 27 =3^3 , violates the theory of prime number

Hence answer must be (D) I & II
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Intern
Joined: 01 Jun 2017
Posts: 25
Re: If x, y, z are distinct prime numbers, which of the following could be  [#permalink]

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20 Aug 2018, 01:10
3
D

1) if x,y and z- 4, 3 and 5. X=4=mean
2) 2*3*5-1=29
3) we require 3 and 9 but 9 is not a prime number. Hence Nopt possible

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Joined: 07 Aug 2018
Posts: 37
Location: Croatia (Hrvatska)
GMAT 1: 560 Q39 V28
Re: If x, y, z are distinct prime numbers, which of the following could be  [#permalink]

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20 Sep 2018, 03:09
gupta335 wrote:
D

1) if x,y and z- 4, 3 and 5. X=4=mean
2) 2*3*5-1=29
3) we require 3 and 9 but 9 is not a prime number. Hence Nopt possible

But 4 isn't a prime so this is not the right example that 1) could be true...
Re: If x, y, z are distinct prime numbers, which of the following could be &nbs [#permalink] 20 Sep 2018, 03:09
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