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Is a product of three integers xyz a prime?

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Is a product of three integers xyz a prime?  [#permalink]

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New post 11 Apr 2018, 09:02
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

53% (00:58) correct 47% (00:33) wrong based on 76 sessions

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Re: Is a product of three integers xyz a prime?  [#permalink]

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New post 11 Apr 2018, 10:41
1
Bunuel wrote:
Is a product of three integers xyz a prime?

(1) x = -y
(2) z = 1


when can be x*y*z be a prime number..
when any TWO of them give us a product of 1 or -1 that is xy or xz or yz is 1 or -1 and the THIRD is a prime number..

(1) x = -y
when x=1, y = -1, so if z is -3...... 1*-1*-3 = 3 Yes
but if x =2 , y =-2, z any other value , ans is NO
insuff

(2) z = 1
nothing about x and y...
insuff

combined..
z=1..
if x = 1 and y = -1 product = -1...No
any other value of x and y will also give a negative integer..
ans is NO always

Suff

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is a product of three integers xyz a prime?  [#permalink]

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New post 22 Apr 2018, 18:22
I) gives -(y^2)*z after putting value in equation

This could give me prime if y=1 and z=-3
And other case also possible so insufficient

II)z=1 yields nothing could be prime ,could not be

Combining both if z=1 then
Eqn become -y^2
It is negative so can't be prime

Ans C

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Re: Is a product of three integers xyz a prime? &nbs [#permalink] 22 Apr 2018, 18:22
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