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If p is a positive integer and r is a negative integer, what

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If p is a positive integer and r is a negative integer, what [#permalink] New post 06 Oct 2006, 09:25
If p is a positive integer and r is a negative integer, what is the value of pr?

1- the sum of p^2 - r^2 is a positive integer.
2- p^r = 1/16
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 [#permalink] New post 06 Oct 2006, 09:50
stat1 : p^2-r^2=+ve integer:

Insufficient..........as we can assume lotsa no's

stat2 : p^r= 1/16

this is possible only in 2 ways:

either p=4, r=-2 or

p=2, r=-4

But if we take both stat's together , then

we can conclude the values of p&r

ans:C
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 [#permalink] New post 06 Oct 2006, 09:50
From hint 2

p ^ r = 16 ^ -1 or 4 ^ -2 or 2 ^ -4
other values are not integer
from this one p * r can be -16 or -8

From hint 1
we get |p| > |r|, so both p = 16 and p = 4 satisfies.

I think it is E
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 [#permalink] New post 06 Oct 2006, 10:02
The debate is b/n E or B. I think E as well, the book says B, pointing out that 4 and -2 or -2 and 4 are the logical answers.

But what about 16 and -1? I mean isn't 16^-1 =1/16?

Help me out here...i think my book's take on this is wrong.
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 [#permalink] New post 06 Oct 2006, 13:45
If p is a positive integer and r is a negative integer, what is the value of pr?

1- the sum of p^2 - r^2 is a positive integer.
2- p^r = 1/16

from one

p^2>r^2....insuff


from two

p^r = 2^-4 or 4^-2 or 16^-1............insuff

my answer is E
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 [#permalink] New post 06 Oct 2006, 14:02
(E) for me too,

Stat 1:
p^2 - r^2 > 0
<=> |p| > |r|

INSUFF

Stat 2:
p^r = 1/16

Since p > 0, we can use the ln fonction:
=> r*ln(p) = -1*ln(16) = -2*ln(4) = -4*ln(2) (r<0)

Thus, the possible couples of (r,p) are (-1;16), (-2;4) and (-4;2). Hence, p*r can be equal to -16 or to -8

INSUFF

Combining (1) with (2),
2 couple of (r,p) remains (-1;16) and (-2;4). Hence, p*r = -16 or = -8

INSUFF
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 [#permalink] New post 06 Oct 2006, 20:15
yezz wrote:
If p is a positive integer and r is a negative integer, what is the value of pr?

1- the sum of p^2 - r^2 is a positive integer.
2- p^r = 1/16

from one

p^2>r^2....insuff


from two

p^r = 2^-4 or 4^-2 or 16^-1............insuff

my answer is E


thanx ...tht was an eye opener
  [#permalink] 06 Oct 2006, 20:15
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