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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: 91
Location: New Zealand
If x, y, z are distinct prime numbers, which of the following could be  [#permalink]

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18 Aug 2018, 23:42
4
00:00

Difficulty:

55% (hard)

Question Stats:

51% (01:15) correct 49% (01:15) wrong based on 140 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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Re: If x, y, z are distinct prime numbers, which of the following could be  [#permalink]

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19 Aug 2018, 00:09
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: 23
Re: If x, y, z are distinct prime numbers, which of the following could be  [#permalink]

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20 Aug 2018, 00:10
4
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

Manager
Joined: 07 Aug 2018
Posts: 109
Location: United States (MA)
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, 02:09
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...
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Re: If x, y, z are distinct prime numbers, which of the following could be  [#permalink]

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21 Sep 2018, 10:08
If x, y, z are distinct prime numbers, which of the following could be true?

I. x is the mean of the three primes.
=>3+5+7/3 = 15/3 = 5 (YES). Hence B & C eliminated.

II. xyz - 1 is a prime
=> 2 x 3 x 5 = 30
=>30-1
=>29 is a prime number (YES). Hence A eliminated

III. 27 is divisible by xyz
=>27/30 = Not divisible
=>27/105 = Not divisible
=>27/385 = Not divisible
=>27/1001 = Not divisible
Hence we proved that (III) is incorrect. So we can eliminate E

Finally we are only left with D
i.e. I & II

Thank you
Arjun
Re: If x, y, z are distinct prime numbers, which of the following could be &nbs [#permalink] 21 Sep 2018, 10:08
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