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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
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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:

55% (hard)

Question Stats:

57% (01:37) correct 43% (01:41) wrong based on 143 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, 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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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
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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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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...
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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, 11:08
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
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Re: If x, y, z are distinct prime numbers, which of the following could be  [#permalink]

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17 Aug 2019, 10:21
1
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

My Approach :
Just write down the initial primes before anything else.
2,3,5,7,11,13,17,19.

I. x is the mean of the three primes. - You can see 5 is the mean of 3,5,7.

II. xyz - 1 is a prime - Try (2*3*5) -1 - 29 is a prime

III. 27 is divisible by xyz - You cannot get 3^3 in the denominator because only one 3 can come from the prime number 3. No Possible.

Hence D .
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Re: If x, y, z are distinct prime numbers, which of the following could be   [#permalink] 17 Aug 2019, 10:21
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