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Is a nonzero integer Z prime? (1) |Z|^|Z|=4 (2) |Z^Z|=Z^2

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SVP
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Is a nonzero integer Z prime? (1) |Z|^|Z|=4 (2) |Z^Z|=Z^2 [#permalink] New post 09 Jun 2003, 23:35
00:00
A
B
C
D
E

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(N/A)

Question Stats:

25% (01:37) correct 75% (00:00) wrong based on 4 sessions
Is a nonzero integer Z prime? :pray

(1) |Z|^|Z|=4
(2) |Z^Z|=Z^2
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 [#permalink] New post 13 Jun 2003, 06:12
KSS wrote:
D. ?


D is ABSOLUTELY wrong. I think it was a blind guess, no?
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 [#permalink] New post 13 Jun 2003, 09:06
I think it is B

a) Z=2 or Z=-2 - not sufficient
b) if Z=2 |Z^Z|=|2^2|=2^2=4; Z^2=4

if Z=-2 |Z^Z|=|(-2)^(-2)|=|(1/-2)^2|=1/4; Z^2=4

so, Z=2 - sufficient
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 [#permalink] New post 13 Jun 2003, 09:32
I like this one, excellent !

Ans : C, Yes

1) Z = 2 or -2

2) Z = 1 or 2

Combined : z = 2
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 [#permalink] New post 13 Jun 2003, 11:29
It is C, but many of you wrong anyway.

(1) Z=2 (prime) or -2 (not prime) Thus, not enough.
(2) Z= 1( not prime), -1 (not prime), 2 (prime), Thus, not OK again.

Combine: Z=2, which is OK. The answer, therefore, is C.

I am shoked guys--you lose and add so many extraneous roots!
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 [#permalink] New post 12 Jul 2003, 18:21
Great problem and great solution!
Is there any rule or trick to make sure one gets all the roots
for an given equation?
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 [#permalink] New post 13 Jul 2003, 11:36
Actually, there is no any special trick for such a question, save for simple checking simple integers, such as 0, 1, -1, 2, -2 and so on.

The most important part of the given question is to remember that 2 is a prime. The smallest one, but a prime even so. 1 and 0 are not primes as are not all negative integers.
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Re: DS: PRIME [#permalink] New post 22 Mar 2011, 19:38
(1)

Z is 2 or -2

So not sufficient

(2)

Z^Z is +ve

|(-1)^-1| = (-1)^2

|1^1| = 1^2 - non-prime

|2^2| = 2^2 - prime

-2 does not fulfil this though

So not sufficient

(1) and (2) together

Z = 2, hence answer is C.
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Re: DS: PRIME [#permalink] New post 22 Mar 2011, 19:50
From 1: Z =2,-2
From 2: z =1,2
So Z=2 (Common terem)
C
Re: DS: PRIME   [#permalink] 22 Mar 2011, 19:50
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Is a nonzero integer Z prime? (1) |Z|^|Z|=4 (2) |Z^Z|=Z^2

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